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A COURSE IN 



MECHANICAL DRAWING. 



BY 



/ 



JOHN S. REID, 

Instructor in Mechanical Drawing and Designing, 

Sibley College, Cornell University, 

Ithaca, N. V. 



FIRST EDITION, 
FIRST THOUSAND. 




NEW YORK. 

JOHN WILEY & SONS. 
London : CHAPMAN & HALL, Limited. 

2?^aPco?Y, 



1898. 



TWO COPIES RECEIVED. 



'b 






>608 



Copyright, 1898, 

BY 

JOHN S. REID. 



ROBERT DRUMMOND, ELECTROTYPER AND PRINTER. NEW YORK. 



PREFACE 



In the course of a large experience as an instructor in 
drawing and designing, the author of this work has often been 
called upon to teach the elements of mechanical drawing to 
students in marine, electrical, railway, and mechanical engi- 
neering. Having tried and failed to find a book on the sub- 
ject that was entirely suitable for his use as a text-book, he 
has found it necessary to prepare the present work. 

This course contains, in the author's judgment, a com- 
plete and concise statement, accompanied by examples, of 
the essential principles of mechanical drawing — all that any 
young man of ordinary intelligence needs to master, by care- 
ful study, the more advanced problems met with in machine 
construction and design. Such works as the author has tried, 
although most excellent from certain standpoints, were either 
incomplete in some of the divisions of the subject or too volu- 
minous and elementary in the treatment of details. 

The author does not imagine this work is perfect, but he 
believes that it comes nearer what is needed in teaching the 
elements of mechanical drawing in technical schools, high 
schools, evening drawing schools, and colleges than any work 
he has examined. 

The chapter on Con\-entions will be appreciated by students 



PREFA CE. 

when called upon to execute working drawings in practical 
work. The methods described are considered by the author 
to be those which have met with general approval by the 
experienced American draftsmen of the present time. 

My acknowledgments are due to E. C. Cleaves, professor 
of drawing, Sibley College, Cornell University, for reading 
the manuscript and making some valuable suggestions. 

The Author. 

April I, 1S9S. 



CONTENTS 



INTRODUCTION. 

PAGE 

The Complete Outfit, Illustrated i 

CHAPTER 1. 

Instruments 7 

Use of Instruments 7 

Pencil 7 

Drawing Pen 9 

Triangles 11 

T Square 11 

Drawing Board .* 11 

Sibley College Scale 12 

Scale Guard 12 

Compasses 13 

Dividers or Spacers 13 

Spring Bows 14 

Irregular Curves 14 

Protractor 14 

CHAPTER 11. 
Geometrical Drawing 16 

CHAPTER III. 
Conventions 56 

CHAPTER IV. 
Lettering and Figuring 64 

CHAPTER V. 

Orthographic Projection 74 

Shade Lines and Shading 103 

Conventions 104 

Shading 106 

Isometrical Drawings 112 

Working Drawings u8 

iii 



MECHANICAL DRAWING. 



INTRODUCTION. 

A NEED has been felt by instructors and students, especially 
in technical courses, for a text-book that would illustrate the 
fundamental principles of mechanical drawing in such a prac- 
tical, lucid, direct and progressive way as to enable the 
instructor to teach, and the student to acquire, the greatest 
number of the essential principles involved, and the ability to 
apply them, in a draftsman-like manner, in the shortest space 
of time. 

With this in mind, the present work has been prepared 
from the experience of the writer, a practical draftsman and 
teacher for over fifteen years. 

THE COMPLETE OUTFIT. 

The complete outfit for students in mechanical drawing in 
Sibley College is as follows : 

(i) The Drawing-board for freshman work is if y^22" 
X f, the same as that used for free-hand drawing. The 
board for sophomore and junior drawing is 20" X 26" X not 
more than \" in thickness. The material should be soft pine 
and constructed as shown by Fig. i. 



MECHANICAL BRA WING. 



(2) Paper, quality and size to suit. 

(3) Pencils, one 6H and one 4H Koh-i-noor or Faber, 
also one Eagle Pilot No. 2 with rubber tip. 

(4) The T-Square for freshman work is furnished by the 




Fig. t. 

department ; a plain pearwood T-square with a fixed head is 
all that is necessary for sophomore or junior work. Length 
to suit drawing-board. 

(5) Instruments. ''The Sibley College Set," shown by 
Fig. 2, was compiled by the writer, and is recommended as a 
first-class medium-priced set of instruments. It contains* 




Fig. 2. 
A Compass, 5^'^ long, with fixed needle-point, pencil, pen 
and lengthening bar. 

A Spring Bow Pencil, 3'' long. 
A '' " Pen, 3'' long. 

A *' " Spacer, 3'' long. 

A Drawing-pen, medium length. 
A Hair-spring Divider, 5" long. 
A nickel-plated box with leads. 



IN TROD UCTION, 3 

(6) A Triangular Boxwood Scale graduated as 

\ , =^ & -^ * 




Fig. 3. 



follows: V' and 2'^ 3'^ and if', i'' and J'', f' and f ', -^V'' and 



5 • 





Fig. 4, 




Fig. 5 



ME CHA NIC A L D KA WING. 

(7) I Triangle 30° x 60°, celluloid, \q" long. Fig. 4. 

I - 45°, '' 7" '' 

(8) "Sibley College Set" of Irregular Curves. 

(9) Glass-paper Pencil Sharpener. 




Fig. 6. 



(10) Ink, black waterproof, S.&H. Fig. 7. 

(11) " red '' Higgins. Fig. 

(12) '' blue 





Fig. 7. 



Fig. 8. 



(13) Ink Eraser, Faber's Typewriter. 

(14) Pencil Eraser, Tower's Multiplex Rubber. Fig. 



IN TRODIX: TION. 5 

(15) Sponge Rubber or Faber's Kneaded Rubber. 
Fie. 10. 



'^'a.->«^sc ^ n»»n:^nw\.xm^ -<?jj»'>e>-^^ts» 






Fig. 9. 

(16) Tacks, a small box of I oz. tacks. 

(17) Water-colors, \ pan each of Payne's Gray, Crim- 
son Lake, Prussian Blue, Burnt Sienna, and Gamboge. Wind- 
sor & Newton. Fig;. 11. 





Fig. 10. Fig. ii. 

(18) Tinting Brush, Camel's Hair No. lo. Fig. 12. 




Fig. 12. 

(19) Tinting Saucer. Fig. 13. 

(20) Water Glass. Fig. 14. 

(21) Arkansas Oil-stone. 2' 

(22) Piece of Sheet Celluloid No. 3000, dull on both 
sides. 



X \" XtV". 



6 



MECHANICAL DRA WING. 



(23) Protractor, German silver, about 5" diam. Fig. 15, 

(24) Scale Guard, '' 





Fig. 13. 



Fig. 14. 



(25) Sheet of Tracing-cloth, 18'' x 24''. 

(26) Writing-pen, point, ''Gillott" No. 303, 




Fig. 15. 



,1, 1, 1, hi, I, Ih, 1, 1, 1. 1, 1, 1,1 

Fig. 16. 



(27) Piece of SHEET BRASS, 4''X4". 

(28) Needles, two with handles. 

The following numbers of '* The Complete Outfit " are 
all that the student will be required to purchase for freshman 
mechanical drawing (No. 2 Register, '97-'98) : 2, 3, 5, 6, 7, 
8, 9, 10, 13, 14, 16, 26. 

The remainder of the outfit may be purchased during the 
sophomore and junior years. 



CHAPTER I. 
INSTRUMENTS. 

It is a common belief among students that any kind of 
cheap instrument will do with which to learn mechanical 
drawing, and not until they have acquired the proper use of 
the instruments should they spend money in buying a first- 
class set. This is one of the greatest mistakes that can be 
made. Many a student has been discouraged and disgusted 
because, try as he would, he could not make a good drawing, 
using a set of instruments with which it would be difficult for 
even an experienced draftsman to make a creditable showing. 

If it is necessary to economize in this direction it is better 
and easier to get along with a fewer number, and have them 
of the best, than it is to have an elaborate outfit of question- 
able quality. 

The instruments composing the ''Sibley College Set" 
are made by T. Alteneder & Sons, and are certainly as good 
as the best. See Fig. 17. 

USE OF INSTRUMENTS. 

TJic Pencil. — Designs of all kinds are usually worked out 
in pencil first, and if to be finished and kept they are inked in 
and sometimes colored and shaded ; but if the drawing is only 
to be finished in pencil, then all the lines except construction, 
center, and dimension lines should be made broad and dark, 

7 



8 MECHANICAL DRAWING. 

SO that the drawing will stand out clear and distinct. It will 
be noticed that this calls for two kinds of pencil-lines, the 
first a thin, even line made with a hard, fine-grained lead- 
pencil, not less than 6H (either Koh-i-noor or Faber's), and 
sharpened to a knife-edge in the following manner: The lead 
should be carefully bared of the wood with a knife for about 
y , and the wood neatly tapered back from that point ; then 
lay the lead upon the glass-paper sharpener illustrated in the 
outfit, and carefully rub to and fro until the pencil assumes a 
long taper from the wood to the point; now turn it over and 
do the same with the other side, using toward the last a 
slightly oscillating motion on both sides until the point has 
assumed a sharp, thin, knife-edge endwise and an elliptical 
contour the other way. 

This point should then be polished on a piece of scrap 
drawing-paper until the rough burr left by the glass-paper is 
removed, leaving a smooth, keen, ideal pencil-point for draw- 
ing straight lines. 

With such a point but little pressure is required in the 
hands of the draftsman to draw the most desirable line, one 
that can be easily erased when necessary and inked in to 
much better advantage than if the line had been made with a 
blunt point, because, when the pencil-point is blunt the incli- 
nation is to press hard upon it when drawing a line. This 
forms a groove in the paper which makes it very difficult to 
draw an even inked line. 

The second kind of a pencil-line is the broad line, as 
explained above ; it should be drawn with a somewhat softer 
pencil, say 4H, and a thicker point. 

All lines not necessary to explain the drawing should be 



INSTRUMENTS. 



erased before inking or broadening the pencil-lines, so as to 
make a minimum of erasing and cleaning after the drawing is 
finished. 

When drawing pencil-lines, the pencil should be held in a 
plane passing through the edge of the T-square perpen- 
dicular to the plane of the paper and making an angle with 
the plane of the paper equal to about 60°. 

Lines should always be drawn from left to right. A soft 
conical-pointed pencil should be used for lettering, figuring, 
and all free-hand work. 

TJic Drawiiig-pcn. — The best form, in the writer's opinion, 
is that shown in Fig. 17. The spring on the upper blade 




Fig. 17. 
spreads the blades sufficiently apart to allow for thorough 
cleaning and sharpening. The hinged blade is therefore 
unnecessary. The pen should be held in a plane passing 
through the edge of the T-square at right angles to the plane 
of the paper, and making an angle with the plane of the 
paper ranging from 60° to 90°. 

The best of drawing-pens will in time wear dull on the 
point, and until the student has learned from a competent 



lO MECHANICAL DRA WING. 

teacher how to sharpen his pens it would be better to have 
them sharpened by the manufacturer. 

It is difficult to explain the method of sharpening a draw- 
ing-pen. 

If one blade has worn shorter than the other, the blades 
should be brought together by means of the thumb-screw, and 
placing the pen in an upright position draw the point to and 
fro on the oil-stone in a plane perpendicular to it, raising and 
lowering the handle of the pen at the same time, to give the 
proper curve to the point. The Arkansas oil-stones (No. 2 1 
of '^ The Complete Outfit ") are best for this purpose. 

The blades should next be opened slightly, and holding 
the pen in the right hand in a nearly horizontal position, place 
the lower blade on the stone and move it quickly to and fro, 
slightly turning the pen with the fingers and elevating the 
handle a little at the end of each stroke. Having ground the 
lower blade a little, turn the pen completely over and grind 
the upper blade in a similar manner for about the same length 
of time ; then clean the blades and examine the extreme 
points, and if there are still bright spots to be seen continue 
the grinding until they entirely disappear, and finish the 
sharpening by polishing on a piece of smooth leather. 

The blades should not be too sharp, or they will cut the 
paper. The grinding should be continued only as long as the 
bright spots show on the points of the blades. 

When inking, the pen should be held in about the same 
position as described for holding the pencil. Many drafts- 
men hold the pen vertically. The position may be varied 
with good results as the pen wears. Lines made with the 
pen should only be drawn from left to right. 



INS TR UMEN TS. 1 1 

THE TRIANGLES. 

The triangles shown at Fig. 4 (in '' The Complete Outfit ") 
are lo'^ and j" long respectively, and are made of transparent 
celluloid. The black rubber triangles sometimes used are but 
very little cheaper (about 10 cents) and soon become dirty 
when in use ; the rubber is brittle and more easily broken than 
the celluloid. 

Angles of 15°, 75°, 30°, 45°, 60°, and 90° can readily be 
drawn with the triangles and T-square. Lines parallel to 
oblique lines on the drawing can be drawn with the triangles 
by placing the edge representing the height of one of them 
so as to coincide with the given line, then place the edge rep- 
resenting the hypotenuse of the other against the corre- 
sponding edge of the first, and by sliding the upper on the 
lower when holding the lower firmly with the left hand any 
number of lines may be drawn parallel to the given line. 

The methods of drawing perpendicular lines and making 
angles with other lines within the scope of the triangles and T- 
square are so evident that further explanation is unnecessary^ 

THE T-SQUARE. 
The use of the T-square is very simple, and is accom- 
plished by holding the head firmly with the left hand against 
the left-hand end of the drawing-board, leaving the right 
hand free to use the pen or pencil in drawing the required 
lines. 

THE DRAWING-BOARD. 
If the left-hand edge of the drawing-board is straight and 
even and the paper is tacked down square with that edge and 



12 MECHAXICAL DRAWING. 

the T-square, then horizontal lines parallel to the upper edge 
of the paper and perpendicular to the left-hand edge may be 
drawn with the T-square, and lines perpendicular to these 
can be made by means of the triangles, or set squares, as they 
are sometimes called. 

THE SIBLEY COLLEGE SCALE. 

This scale, illustrated in Fig. 3 (in *' The Complete Out- 
fit "), was arranged to suit the needs of the students in Sibley 
College. It is triangular and made of boxwood. The six 
edges are graduated as follows; yV" or full size, ■^-^'' , i" 
and I" = I ft., \" and \" = i ft., 3'' and ij" = i ft., and 
4" and 2" = I ft. 

Drawings of very small objects are generally shown en- 
larged — e.g., if it is determined to make a drawing twice the 
full size of an object, then where the object measures one inch 
the drawing would be made 2", etc. 

Larger objects or small machine parts are often drawn full 
size — i.e., the same size as the object really is — and the draw- 
ing is said to be made to the scale of full size. 

Large machines and large details are usually made to a 
reduced scale — e.g., if a drawing is to be made to the scale of 
2" = I ft., then 2" measured by the standard rule would be 
divided into 12 equal parts and each part would represent i'\ 
See Fig. 8i(^. 

THE SCALE GUARD. 

This instrument is shown in Fig. 16 (in "The Complete 
Outfit"). It is employed to prevent the scale from turning, 
so that the draftsman can use it without havins^ to look for 



INSTRUMEiVTS. 13 

the particular edge he needs every time he wants to lay off 
a measurement. 

THE COMPASSES. 

When about to draw a circle or an arc of a circle, take 
hold of the compass at the joint with the thumb and two first 
fingers, guide the needle-point into the center" and set the 
pencil or pen leg to the required radius, then move the thumb 
and forefinger up to the small handle provided at the top of 
the instrument, and beginning at the lowest point draw the 
line clockwise. The weight of the compass will be the only 
down pressure required. 

The sharpening of the lead for the compasses is a very im- 
portant matter, and cannot be emphasized too much. Before 
commencing a drawing it pays well to take time to properly 
sharpen the pencil and the lead for compasses and to keep 
them always in good condition. 

The directions for sharpening the compass leads are the 
same as has already been given for the sharpening of the 
straight-line pencil. 

THE DIVIDERS OR SPACERS. 

This instrument should be held in the same manner as de- 
scribed for the compass. It is very useful in laying off equal 
distances on straight lines or circles. To divide a given line 
into any number of equal parts with the dividers, say 12, it 
is best to divide the line into three or four parts first, say 4, 
and then when one of these parts has been subdivided accu- 
rately into three equal parts, it will be a simple matter to 
steo off these latter divisions on the remaining three-fourths 



14 MECHANICAL DRA WING. 

cf the given line. Care should be taken not to make holes in 
the paper with the spacers, as it is difficult to ink over them 
without blotting. 

THE SPRING BOWS. 

These instruments are valuable for drawing the small cir- 
cles and arcs of circles. It is very important that all the 
small arcs, such as fillets, round corners, etc., should be care- 
fully pencilled in before beginning to ink a drawing. ]\Iany 
good drawings are spoiled because of the bad joints between 
small arcs and straight lines. 

When commencing to ink a drawing, all small arcs and 
small circles should be inked first, then the larger arcs and 
circles, and the straight lines last. This is best, because it is 
much easier to know where to stop the arc line, and to draw 
the straight line tangent to it, than vice versa. 



IRREGULAR CURVES. 

The Sibley College Set of Irregular Curves shown in Fig. 
5 are useful for drawing irregular curves through points that 
have already been found by construction, such as ellipses, 
cycloids, epicyloids, etc., as in the cases of gear-teeth, cam 
outlines, rotary pump wheels, etc. 

When using these curves, that curve should be selected 
that will coincide with the greatest number of points on the 
line required. 

THE PROTRACTOR. 

This instrument is for measuring and constructing angles. 
It is shown in Fig. 15. It is used as follows when measuring 



IXSTRLWEXTS. 1 5 

an angle : Place the lower straight edge on the straight line 
Avhich forms one of the sides of the angle, with the nick 
•exactly on the point of the angle to be measured. Then the 
number of degrees contained in the angle may be read from 
the left, clockwise. 

In constructing an angle, place the nick at the point from 
which it is desired to draw the angle, and on the outer circum- 
ference of the protractor, find the figure corresponding to the 
number of degrees in the required angle, and mark a point on 
the paper as close as possible to the figure on the protractor; 
after removing the protractor, draw a line through this point 
to the nick, which will give the required angle. 



CHAPTER II. 
GEOMETRICAL DRAWING. 

The following problems are given to serve a double pur- 
pose : to teach the use of drawing instruments, and to point 
out those problems in practical geometry that are most useful 
in mechanical drawing, and to impress them upon the mind of 
the student so that he may readily apply them in practice. 

The drawing-paper for this work should be divided tem- 
porarily, with light pencil-lines, into as many squares and rec- 
tangles as may be directed by the instructor, and the drawings 
made as large as the size of the squares will permit. The 
average size of the squares should be not less than 4". When 
a sheet of drawings is finished these boundary lines may be 
erased. 

It will be noticed in the illustrations of this chapter that 
all construction lines are made very narrow, and given and 
required lines quite broad. This is sufficient to distinguish 
them, and employs less time than would be necessary if the 
construction lines were made broken, as is often the case. 

If time will permit, it is advisable to ink in some of these 

drawings toward the last. In that event, the given lines may 

be red, the construction lines blue, and the required lines 

black. 

But even when inked in in black, the broad and narrow 

16 



GEOMETRICAL DRAWING. I 7 

lines would serve the purpose very well without the use of col- 
ored inks. 

The principal thing to be aimed at in making these draw- 
ings is accuracy of construction. All dimensions should be 
laid off carefully, correctly, and quickly. Straight lines join- 
ing arcs should be exactly tangent, so that the joints cannot 
be noticed. It is the little things like these that make or mar 
a drawing, and if attended to or neglected they will make or 
mar the draftsman. The constant endeavor of the student 
should be to make every drawing he begins more accurate, 
quicker and better in every way than the preceding one. 

A drawing should never be handed in as finished until the 
student is perfectly sure that he cannot improve it in any way 
whatever, for the act of handing in a drawing is the same, or 
should be the same, as saying This is the best that I can do ; 
I cannot improve it ; it is a true measure of my ability to 
make this drawing. 

If these suggestions are faithfully followed throughout this 
course, success awaits any one who earnestly desires it. 

Fig. 1 8. To Bisect a Finite Straight Line. — With 
A and^ in turn as centers, and a radius greater than the half 
of AB, draw arcs intersecting at E and i^. Join j5"i^ bisect- 
ing AB at C. 

An arc of a circle may be bisected in the same way. 

Fig. 19. To Erect a Perpendicular at the End of 
THE Line. — Assume the point E above the line as center and 
radius EB describe an arc CBD cutting the line AB in the 
pomt C. From C draw a line through E cutting the arc in 
D. Draw DB the perpendicular. 

Fig. 20. The Same Problem: a Second Method. — 



i8 



ME CHA NIC A L DRA WING. 



With center B and any radius as BC describe an arc CDE 
with the same radius; measure off the arcs CD 2.Vi<\DE. With 
C and D as centers and any convenient radius describe arcs in- 
tersecting at F. FB is the required perpendicular. 




Fig. 21. 

Fig. 2 1. To Draw a Perpendicular to a Line 
FROM A Point above or below It. — Assume the point 
C above the hne. With center C and any suitable radius 
cut the line AB in E and F. From E and F describe arcs 
cutting in D. Draw CD the perpendicular required. 



GEOMETRICAL DRAWING, 



19 



* Fig. 22. To Bisect a Given Angle. — With A as center 
and any convenient radius describe the arc BC. With B and 
C as centers and any convenient radius draw arcs intersecting 
at D. Join AD, then angle BAD = an^rle DAC. 




Fig. 22. 

Fig. 23. To Draw a Line Parallel to a Given 
Line AB Through a Given Point C. — From any point 
on AB dis B with radius BC describe an arc cutting AB in A, 
From A with the same radius describe arc BD. From B with 
AC a.s radius cut arc BD in D. Draw CD. Line CD is paral- 
lel to AB. 




Fig. 23. 

Fig. 24. From a Point D on the Line DE to set 
OFF AN Angle equal to the given Angle BAC. — From 



20 



MECHAXICAL DRA WING. 



A v\-ith any convenient radius describe arc BC. From D with 
the same radius describe arc EF. With center E and radius 
BC cut arc EF in F. Join DF. Angle EDF is = angle BAC. 




Fig. 24. 

Fig. 25. To Divide ax Angle into two equal 
Parts, when the Lines do not Extend to a Meeting 
Point. — Draw the line CD and CE parallel and at equal dis- 




Fig. 25. 

tances from the lines AB and EG. With C as center and any 
radius draw arcs 1,2. With i and 2 as centers and any con- 



GEOMETRICAL DRAWIXG. 21 

venient radius describe arcs intersecting 2XH. A line through 
C and H divides the angle into two equal parts. 

Fig. 26. To Construct a Rhomboid having Adja- 
cent Sides equal to two Given Lines AB and AC, and 
AN Angle equal to a Given Angle A. — Draw line DE 
equal to AB. Make D — angle A. Make DF = AC. From 
/^ with line AB as radius and from £ with line AC 3.s radius 
describe arcs cutting in G. Join FG and EG. 




Fig. 27. To Divide the Line AB into anv Number 
OF EQUAL Parts, sav 15. — Draw a line CD parallel to AB, 
of any convenient length. From C set off along this line the 
number of equal parts into which the line ^i)' is to be divided. 
Draw CA and FB and produce them until they intersect at 
E. Through each one of the points i, 2, 3, 4, etc., draw 
lines to the point E, dividing the line AB into the required 
number of equal parts. 

This problem is useful in dividing a line when the point 
required is difHcult to find accurately — e.g., in Fig. 28 AB is 
the /)itc/i of the spur gear, partly shown, which includes a 



22 



MECHANICAL DRA WING. 



space and a tooth and is measured on the pitch circle. In 
cast gears the space is made larger than the thickness of the 
tooth, the proportion being about 6 to 5 — i.e., if we divide 
the pitch into eleven equal parts the space will measure -f-^ 




3^CP^ 



1 -2, 3 4 5 6 7 8. 9 101112 13 lA IT 
Fig. 27. 




Fig 2S. 



and the tooth -^j. The yV which the space is larger than the 
tooth is called the backlash. Let A' B' be the pitch chord of 
the arc AB. Draw CD parallel to A'B' at any convenient 
distance and set off on it 1 1 equal spaces of any convenient 
length. Draw CA' and DB' intersecting at E. From point 
5 draw a line to ii which w^ill divide A'B' as required; the 
one part -fj and the other y\-. 

Fig. 29. To Divide a Given Line into any Number 
OF Equal Parts: Another Method. — Let AB be the 
given line. From A draw AC d.t any angle, and lay off on it 
the required number of equal spaces of any convenient length. 
Join CB and through the divisions on AC drsiw lines parallel 
to CB, dividing^i5 as required in the points 1', 2', 3^ 4', etc. 

Fig. 30. To Divide a Line AB Proportionally to 
the Divided Line CD. — Draw AB parallel to CD at any 



GEOMETRICAL DRA WING. 



23 



distance from it. Draw lines through CA and /^^ and produce 
them till they meet at E. Draw lines from E through the 
divisions i, 2, 3, 4, etc., of line CD, cutting line AB in the 




A 1 2 3 4 5 fj 7 8 9 10 111213 U B 
Fig. 2q. 

points 5, 6, 7, 8, etc. The divisions on AB will have the 
same proportion to the divisions on CD that the whole line 
AB has to the whole line CD — i.e., the lines will be propor- 
tionally divided. 

E 




Fig. 31. The Same: Another Method. — Let BC, 
the divided line, make any angle with BA, the line to be di- 



24 



MECHANICAL DRAWING. 



vided at B. Draw line CA joining the two ends of the Hnes. 
Draw lines from 5, 6, 7, 8, parallel to CA^ dividing line AB 
in points i, 2, 3, 4, proportional to BC. 

Fig. 32. To Construct an Equilateral Triangle 
ON A Given Base AB. — From the points A and B with AB 
as radius describe arcs cutting in C. Draw lines AC and BC. 
The triangle ABC is equilateral and equiangular. 




Fig. 3 



Fig. 33. To Construct an Equilateral Triangle 
OF A Given Altitude, AB, — From both ends oi AB draw 
lines perpendicular to it as CA and DB. From A with any 
radius describe a semicircle on CA and with its radius cut off 
arcs I, 2. Draw lines from A through i, 2, and produce 
them until they cut the base BD. 

Fig. 34. To Trisect a Right Angle ABC. — From 
the angular point B with any convenient radius describe an 
arc cutting the sides of the angle in C and A. From C and A 
with the same radius cut off arcs i and 2. Draw lines iB and 
2B, and the right angle will be trisected. 



GEOMETRICAL DRAWING. 



25 



Fig. 35. To Construct any Triangle, its Three 
Sides AB and (Seeing given. — From one end of the base 
as A describe an arc with the Hne B as radius. From the 
other end with hne C as radius describe an arc, cutting the 
first arc in D. From D draw Hnes to the ends of Hne A, and a 
triangle will be constructed having its sides equal to the sides 
given. To construct any triangle the two shorter sides B and 
C must together be more than equal to the largest side A. 




Fig. 36. 



Fig. 37. 



Fig. 36. To Construct a Square, its Base AB 
BEING GIVEN. — Erect a perpendicular at B. Make BC equal 



26 



MECHANICAL DRA WING. 



to AB. From A and C with radius AB describe arcs cutting; 
in D. Join DC and DA. 

Fig. 37. To Construct a Square, given its Di- 
agonal AB. — Bisect AB in C. Draw DF perpendicular to- 
AB at C. Make CD and (T/^ each equal to CA. Join ^Z^,, 
Z>i5, ^5/^; and FA. 

Fig. 38. To Construct a Regular Polygon of any 
Number of Sides, the Circumscribing Circle being 
GIVEN. — At any point of contact, as C, draw a tangent AB 
to the given circle. From C with any radius describe a semi- 
circle cutting the given circle. Divide the semicircle into as 
many equal parts as the polygon is required to have sides, as 
I, 2, 3, 4, 5, 6. Draw lines from C through each division, 
cutting the circle in points which will give the angles of the 
polygon. 

D 





Fig. 39. Another Method. — Draw a diameter AB of 
the given circle. Divide AB into as many equal parts as 
the polygon is to have sides, say 5. From A and B with the 



GEOMETRICAL DRAWING. 



27 



line AB as radius describe arcs cutting in C, draw a line from 
C through the second division of the diameter and produce it 
cutting the circle in D. BD will be the side of the required 
polygon. The line C must 'always be drawn through the 
second division of the diameter, whatever the number of 
sides of the polygon. 

Fig. 40. To Construct any Regular Polygon 
^VITII A Given Side AB. — Make BD perpendicular and 
equal to AB. With B as center and radius AB describe arc 
DA. Divide arc DA into as many equal parts as there are 
sides in the required polygon, as i, 2, 3, 4, 5. Draw B2, 
Bisect line AB and erect a perpendicular at the bisection cut- 
ting B2 in C. With C as center and radius CB describe a 
circle. With AB as a chord step off the remaining sides of 
the polygon. 





Fig. 40. 



Fig. 41. 



Fig. 41. Another Method. — Extend hne AB. With 
center A and any convenient radius describe a semicircle. 
Divide the semicircle into as many equal parts as there are 
sides in the required polygon, say 6. Draw lines through 
every division except the first. With A as center and AB as 



28 



MECHANICAL DRA WING. 



radius cut off A2 in C. From C with the same radius cut Ai 
in D. From Z), ^4 in ^. From B, As in F. Join AC, CD, 
DE, £F, and FB. 

Fig. 42. To Construct a Regular Heptagon, the 
Circumscribing Circle being given. — Draw a radius AB. 
With B as center and BA as radius, cut the circumference in 
1,2; it will be bisected by the radius in C. Ci or C2 is equal 
to the side of the required heptagon. 




Fig. 42. 




Fig. 43. To Construct a Regular Octagon, the 
Circumscribing Circle being given. — Draw a diameter 
AB. Bisect the arcs AB in C and D. Bisect arcs CA and 
CB in I and 2. Draw lines from i and 2 through the center 
of the circle, cutting the circumference in 3 and 4. Join Ai, 
iC, C2, 2B, Bi, etc. 

Fig. 44. To Construct a Pentagon, the Side AB 
being given. — Produce AB. With B as center and BA as 
radius, describe arc AD2. With center A and same radius, 
describe an arc cutting the first arc in D. Bisect AB in E. 



GEOMETRICAL DRAWING. 



29 



[' Draw line DE, Bisect arc BD in F. Draw line EF. With 
■' center C and radius EF q.v\\. off arc C\ and i, 2 on the semi- 
' circle. Draw line B2 ; it will be a second side of the penta- 




gon. Bisect it and draw a line perpendicular to it at the 
bisection. The perpendiculars from the sides AB and B2 
will cut in G. With G as center and radius GA describe a 
circle • it will contain the pentagon. 




Fig. 45. 



30 



MECHANICAL DRA IVIXG. 



Fig. 45. To Construct a Heptagon on a Given 
Line AB. — Extend line AB to C7. From B with radius AB 
describe a semicircle. With center A and same radius de- 
scribe an arc cutting the semicircle in D. Bisect AB in E. 
Draw line DE. With C as center and DE as radius, cut off 
arc I on the semicircle. Draw line Bi ; it is a second side of 
the heptagon. Bisect it and obtain the center of the circum- 
scribing circle as in the preceding problem. 

Fig. 46. To Inscribe an Octagon in a Given 
Square. — Draw diagonals AD, CB intersecting at O. From 
A, B, C, and D with radius equal to AO describe quadrants 
cutting the sides of the square in i, 2, 3, 4, 5, 6, 7, 8. Join 
these points and the octagon will be inscribed. 





Fig. 46. 

Fig. 47. To Construct a Regular Octagon on a 
Given Line AB. — Extend line ^^ in both directions. Erect 
perpendiculars at ^ and B. With centers A and B and radius 
^^ describe the semicircle CEB and AF2. Bisect the quad- 
rants CE and DF in i and 2, then Ai and B2 will be two 
more sides of the octagon. At i and 2 erect perpendiculars 
I, 3 and 2, 4 equal to AB. Draw 1-2 and 3-4. Make the 



GEOMETRICAL DRAWING. 



31 



perpendiculars at A and B equal to 1-2 or 3-4 — viz., A^ and 
B6. Complete the octagon by drawing 3-5, 5-6, and 6-4. 

Fig. 48. To Draw a Right Line Equal to Half 
THE Circumference of a Given Circle. — Draw a diam- 
eter AB. Draw line AC perpendicular to AB and equal to 
three times the radius of the circle. Draw another perpen- 
dicular at B to AB. With center B and radius of the circle 
cut off arc BD, bisect it and draw a line from the center of 
the circle through the bisection, cutting line B in E. Join 
EC. Line EC will be equal to half the circumference of 
■circle A. 

G 

A C 




Fig. 49. To Find a Mean Proportional to two 
Given Right Lines. — Extend the line AB to E making BE 
equal to CD. Bisect AE in F. From /^ with radius BA de- 
scribe a semicircle. At B where the two given lines are 
joined erect a perpendicular to AE cutting the semicircle in 
G. BG will be a mean proportional to CD and AB. 

Fig. 50. To Find a Third Proportional (less) to 
TWO Given Right Lines AB and CD. — Make EF= the 
given line AB. Draw EG making an angle with EF ^ DC. 
Join EG. From E with EG as radius cut EF in H. Draw 



32 



MECHANICAL DRA WING. 



H parallel to FG, cutting EG in /. EI is the third propor- 
tional (less) to the two given lines. 





Fig. 50. 



F 

Fig. 51. 



Fig. 51. To Find a Fourth Proportional to three 
Given Right Lines AB, CD, and .5"/^.— Make 6^//= the 
given line AB. Draw GI = CD, making any convenient 
angle to GH. Join HI. From G lay off GH = EF. From 
K draw a parallel to HI cutting GI in L. GL is the fourth 
proportional required. 





Fig. 52. Fig. 53- 

Fig. 52. To Find the Center of a Given Arc ABC. 
— Draw the chords AB and CD and bisect them. Extend 
the bisection lines to intersect in D the center required. 



GEOMETRICAL DRAWING. 



33 



Fig. 53. To Draw a Line Tangent to an Arc of a 
Circle. — (ist.) When the center is not accessible. Let B 
be the point through which the tangent is to be drawn. 
From B lay off equal distances as BE^ BF. Join EF and 
through B draw ABC parallel to EF. (2d.) When the cen- 
ter D is given. Draw BD and through B draw ABC perpen- 
dicular to BB. ABC is tangent to the circle at the point B. 

Fig. 54. To Draw Tangents to the Circle C from 
THE Points without It. — Draw ^6^ and bisect it in ^. . 
From E with radius EC describe an arc cutting circle C in B 
and B. Join CB, CD. Draw AB and AB tangent to the 
circle C. 





Fig. 54- Fig. 55. 

Fig. 55. To Draw a Tangent between two Cir- 
cles. — Join the centers A and B. Draw any radial line 
from A as A2 and make 1-2 — the radius of circle B. From 
A with radius A-2 describe a circle C2D. From center B 



34 



ME CHA NIC A L DRA WING. 



draw tangents BC and BD to circle C2D at the points C and 
D by preceding problem. Join AC and AD and through 
the points E and F draw parallels FG and EH to BD and ^C. 
/^6^ and EH are the tangents required. 

Fig. 56. To Draw Tangents to two Given Cir- 
cles A AND B. — Join A and B. From ^4 with a radius 
equal to the difference of the radii of the given circles de- 





FlG. 56. 

scribe a circle GF. From B draw the tangents BE and BG, 
by Prob. 37. Draw AF and AG extended to E and H. 
Through E and // draw EC and //i^ parallel to BF and ^6^ 
respectively. EC and DH z.x^ the tangents required. 

Fig. 57. To Draw an Arc of a Circle of Given 
Radius Tangent to two Straight Lines. — AB and AC 
are the two straight lines, and r the given radius. At a dis- 
tance — r draw parallels 1-2 and 3-4 to AC and AB, inter- 



GEOMETRICAL DRAWING. 



35 



seating at F. From F draw perpendiculars FD and FE. 
With F as center and FD or FE as radius describe the re- 
quired arc, which will be tangent to the two straight lines at 
the points D and E. 

Fig. 58. To Draw an Arc of a Circle Tangent 
TO TWO Straight Lines BC and CD when the Mid- 
position G IS GIVEN. — Draw CA the bisection of the angle 
BCD and EF at right angles to it through the given point G. 
Next bisect either of the angles FEB or FED. The bisection 
line will intersect the central line CA at A, which will be the 
center of the arc. From A draw perpendiculars Ai and A2, 
and with either as a radius and A as center describe an arc 
which will be tangent to the lines BC and CD at the points i 
and 2. 




Fig. 59. To Inscribe a Circle within a Triangle 
ABC. — Bisect the angles A and B. The bisectors will meet 
in D. Draw D\ perpendicular to AB. Then with center D 
and radius =z Di describe a circle which will be tangent to 
the given triangle at the points i, 2, 3. 

Fig. 60. To Draw an Arc of a Circle of Given 
Radius i^ tangent to two Given Circles A and B. — 
From A and B draw any radial lines as ^3, B4.. Outside 
the circumference of each circle cut off distances 1-3 and 2-4 



36 



MECHAXICAL DRA WING. 



each 



the given radius R. Then with center A and radius 



^-3, and center B and radius B-^ describe arcs intersecting at 
C. Draw CAXB cutting the circles at 5 and 6. With centre 
C and radius (^5 or C6 describe an arc which will be tangent 
at points 5 and 6. 

p — ^ 




Fig. 60. 



Fig. 61. To Draw ax Arc of a Circle of Given 
Radius R tangent to two Given Circles A and B 




Fig 61. 



WHEN THE Arc includes the Circles. — Through A and B 
draw convenient diameters and extend them indefinitely. On 



GEOMETRICAL DRAWING. 



37 



these measure off the distances 1-2 and 3-4, each equal in 
length to the given radius R. Then with center A and radius 
A2, center B and radius ^4, describe arcs cutting at C. From 
C draw C^ and (76 through B and A. With center C and ra- 
dius C6 or 6^5 describe the arc 6, 5, which will be tangent to 
the circles at the points 6 and 5. 

Fig. 62. To Draw an Arc of a Circle of Given 
Radius R tangent to Two Given Circles A and B 
WHEN THE Arc includes one Circle and excludes the 
other. — Through A draw any diameter and make 1-2 = R. 




Fig. 62. 



From B draw any radius and extend it, making 3-4 = R. With 
center A and radius A2 and center B and radius Ba^ describe 
arcs cutting at C. With C as center and radius = C^ or (76 
describe the arc 5, 6. 

Fig. 63. Draw an Arc of a Circle of Given Ra- 
dius R TANGENT TO A STRAIGHT LiNE AB AND A CIRCLE 
CD. — From £", the center of the given circle, draw an arc of a 



38 



MECHANICAL DRA WING. 



circle i, 2 concentric with CD at a distance R from it, and 
also a straight line 3, 4 parallel to AB at the same distance R 
from AB, Draw ^(9 intersecting CD at 5. Draw the perpen- 
dicular 06. With center O and radius (96 or O^ describe the 
required arc. 









^ 


A 




e 


"""^'^^1 5 




^ 


~^^ 


ft^ 


A 


\ 


X\ 


.^^"^1 -^ 




Fig. 63. 

Fig. 64. To Describe an Ellipse Approximately 
BY means of three Radii (F. R. Honey's method). — 




Fig. 64. 

Draw straight lines RH a.nd NQ, making any convenient angle 
at H. With center H and radii equal to the semi-minor and 



GEOMETRICAL DRAWING. 



39 



semi-major axes respectively, describe arcs LM and NO. Join 
LO and draw MK and NP parallel to LO. Lay off Zi —\ 
of LX. Join Oi and draw M2 and ^¥3 parallel to Oi. Take 
//'3 for the longest radius (= Z), //2 for the shortest radius 
(= E\ and one-half the sum of the semi-axes for the third 
radius (== 5), and use these radii to describe the ellipse as 
follows: Let AB and CD be the major and minor axes. Lay 
off ^4 = Z" and ^5 = S. Then lay o'^ CG = T and C^ = S. 



With G as center and G6 as radius draw the arc 6, 



With 



center 4 and radius 4, 5, draw arc 5, ^, intersecting 6, ^ at ^. 
Draw the line G^- and produce it making GS = T. Draw ^, 
4 and extend it to 7 making ^, 7 =: 5. With center G and 
radius GC {=T) draw the arc (78. With center ^ and radius 
g^ 8 (=5) draw the arc 8, 7. With center 4 and radius 4, 7 
{= £) draw arc 7^. The remaining quadrants can be drawn 
in the same way. 

Fig. 65. To Draw ax Ellipse havixg given the 
Axes yi^ AND CD. — Draw AB and CD at right angles to and 
bisecting each other at E. With center C and radius EA cut 
AB in E and E' the foci. Divide EE or EE' into a number of 
parts as shown at i, 2, 3, 4, etc. Then with /^ and E' as cen- 





^U 


^<^ 


iWl 




*fr^ 




^'^?*''A 


f 




^r^^^\ 


.ifry 


t 


r 


1 i77>r>I'^V 








12 3 Jt 5 67 j 


\^ 


H^ 




Ccm-E,A'o.o i^ 




^>tr 


^^e^ 


-^^^"^ 



Fig. 65. 




Fig. 67. 



ters and Ai and ^i, and ^2 and B2, etc., as radii describe arcs 
intersecting in R, S, etc., until a sufficient number of points 



40 



ME CHA XICA L DRA WIXG. 



are found to draw the elliptic curve accurately throughout. 
(No. 5 of the ''Sibley College Set" of irregular curves is 
very useful in drawing this curve.) To draw a tangent to 
the ellipse at the point G\ Extend FG and draw the bisector 
of the angle HGF . KG is the tangent required. 

Fig. 6^, Another Method. — Let yJ^ and AC h& the 
semi axes. With A as center and radii AB and AC describe 
circles. Draw any radii as ^3 and ^^4, etc. Make 3 i, 42, 
etc., perpendicular to AB, and D2, E^, etc., parallel to AB. 
Then i, 2, 5, etc., are points on the curve. 

Fig. Gy. Another ^Method. — Place the diameters as 
before, and construct the rectangle CDEF. Divide AB and 
DB and BF into the same number of equal parts as I, 2, 3 and 
B. Draw from C through points i, 2, 3 on AB and BD 
lines to meet others drawn from E through points i, 2, 3 on 
A^B and FB intersecting in points GHK. GHK are points on 
the curve. 

Fig. 68. Another Method. — Place the diameters AB 
and CD as shown in Drawing Xo. i. Draw any convenient 
'1 




Fig. 68. 



angle RHQ. Drawing No. 2. With center //"and radii equal 
to the semi-minor and semi-major axes describe arcs LM and 



GEOMETRICAL DRAWING. 4 1 

NO. Join LO and draw MK and NP parallel to LO. Then 
from C and D with a distance = HP lay off the points i i' on 
the minor axis and from A and B with a distance = HK lay 
off the points 2 2' on the major axis. With centers 1,1', 2 and 
2' and radii \—D and 2-B, respectively, draw arcs of circles. 
On a piece of transparent celluloid 7" lay off from the point G, 
GF and GE = the semi-minor and semi-major axes respec- 
tively. Place the point i^on the major axis and the point E on 
the minor axis. If the strip of celluloid is now moved over 
the figure, so that the point E is always in contact with the 
semi-minor axis and the point F with the semi major axis, the 
necessary number of points may be marked through a small 
hole in the celluloid at G with a sharp conical-pointed pencil, 
and thus complete the curve of the ellipse between the arcs of 
circles. 

Fig. 69. To Construct a Parabola, the Base CD 
AND THE Abscissa AB being given. — Draw EF through A 
parallel to CD and CE and DF parallel to AB. Divide AE, 
AF, EC, and FD into the same number of equal parts. 
Through the points i, 2, 3 on ^i^ and AE draw lines parallel 
to AB, and through A draw lines to the points 1,2, 3 on FD 
and EC intersecting the parallel lines in points 4, 5, 6, etc., of 
the curve. 

Fig. 70. Given the Directrix BD and the Focus C 
TO Draw a Parabola and a Tangent to It at the Point 
3. — The parabola is a curve such that every point in the curve 
is equally distant from the directrix j5Z> and the focus C. The 
vertix E is equally distant from the directrix and the focus, 
i.e. CE is = EB. Any line parallel to the axis is a diameter. 
A straight line drawn across the figure at right angles to the 



42 



MECHANICAL DRA WIXG. 



axis is a double ordinate, and either half of it is an ordinate. 
The distance from C to any point upon the curve, as 2 is 
always equal to the horizontal distance from that point to the 
directrix. Thus Ci ^^ i, i' , C2 to 2, 2', etc. Through C 
draw ACF at right an2:les to BD, ACF is the axis of the 



Ai i 3 F 




/ 


S 


^ 


\ 


1 


I 




\ 


D 


A 


^ 


G 


5 









I 


i 


\ 


3 






4 



Fig. 70. 

curve. Draw parallels to BD through any points in AB^ and 
with center C and radii equal to the horizontal distances of 
these parallels from BD describe arcs cutting in the points i, 
2, 3, 4, etc. These are points in the curve. The tangent to 
the curve at the point 3 may be drawn as follows: Produce 
AB to F. Make FF = the horizontal distance of ordinate 33 
from F. Draw the tangent through 2,F. 

Fig. 71. To Draw an Hyperbola, having given 
THE Diameter AB, the Abscissa BD, and Double Ordi- 
nate FF. — Make F4. parallel and equal to BD. Divide DF 
and F^ into the same number of equal parts. From B draw 
lines to the points in /[F and from A draw lines to the points 
in DF. Draw the curve through the points where the lines 
correspondingly numbered intersect each other. 



GEOMETRICAL DRAWING. 



43 



Fig. ^2. To Construct an Oval the Width AB 
BEING GIVEN.— Bisect AB by the line CD in the point E, 
and with E as center and radius EA draw a circle cutting CD in 





Fig. 71, 



Fig. 72. 



F. From ^ and ^draw lines through F. From A and B with 
radius equal to AB draw arcs cutting the last two lines in G 
and H. From F with radius /^6^ describe the arc GH to meet 
the arcs AG and ^5//, which will complete the oval. 

Fig. 73. Given an Ellipse to Find the Axes and 
Foci. — Draw two parallel chords AB and CD. Bisect each 
of these in E and F. Draw EF touching the ellipse in i and 
2. This line divides the ellipse obhquely into equal parts. 
Bisect I, 2 in 6^, which will be the center of the ellipse. From 
G with any radius draw a circle cutting the ellipse in HIJK. 
Join these four points and a rectangle will be formed in the 
ellipse. Lines LM and NO, bisecting the sides of the 
rectangle, will be the diameters or'axes of the ellipse. With 
iV or (9 as centers and radius = GL the semi-major axis, de- 
scribe arcs cutting the major axis in P and Q the foci. 

Fig. 74. To Construct a Sipral of one Revolu- 
tion. — Describe a circle using the widest limit of the spiral as 



44 



MECHANICAL DRA WING. 



a radius. Divide the circle into any number of equal parts as 
A., B, C, etc. Divide the radius into the same number of equal 
parts as i to 12. From the center with radius 12, i describe 
an arc cutting- the radial line B in i' . From the center con- 
tinue to draw arcs from points 2, 3,4, etc., cuttingthe corre- 
sponding radii C, D, E, etc. in the points 2', 3', 4', etc. From 
12 trace the Archimedes Spiral of one revolution. 







X 


A 






H 


^ 




^ 


\^ 


K 


/I 




^^ 


\y 


XK 


\\^ 




' 


\ \ 


y\ 




/ 1 1 


% 


^ 


K 


\G\ 




7/ 


I 


VCi 


^:^^ 


_i 


v-^ 


V 




Fig. 73. 

Fig. 75. To Describe a Spiral of any Number of 
Revolutions, e.g., 2. — Divide the circle into any num- 
ber of equal parts d^s A, B, C, etc., and draw radii. Divide 
the radius ^12 into a number of equal parts corresponding 
with the required number of revolutions and divide these 
into the same number of equal parts as there are radii, viz., 
I to 12. It will be evident that the figure consists of two 
separate spirals, one from the center of the circle to 12, and 
one from 12 to A. Commence as in the last problem, draw- 
ing arcs from i. 2, 3, etc., to the correspondingly numbered 
radii, thus obtaining the points marked i\ 2', 3', etc. The 
first revolution completed, proceed in the same manner to 
find the points i^\ 2" , 3'', etc. Through these points trace 
the spiral of two revolutions. 



GEOMETRICAL DRAWING. 



45 



Fig. 'j^. To Construct the Involute of the Chi- 
cle O. — Divide the circle into any number of equal parts 
and draw radii. Draw tangents at right angles to these radii. 
On the tangent to radius i la)- off a distance equal to one 
of the parts into which the circle is divided, and on each of 

A 





the tangents set off the number of parts corresponding to the 
number of the radii. Tangent 12 will then be the circumfer- 
ence of the circle unrolled, and the curve drawn through the 
extremities of the other tangents will be the involute. 

Fig. -jj. To Describe an Ionic Volute. — Divide the 
given height into seven equal parts, and through the point 3 
the upper extremity of the third division draw 3, 3 perpen- 
dicular to AB, From any convenient point on 33 as a cen- 
ter, with radius equal to one-half of one of the divisions on 
AB, describe the eye of the volute NPNM, shown enlarged 
at Drawing No. 2. iVTV corresponds to line 3, 3, Drawing 
No. I. Make PM perpendicular to AW and inscribe the 
square AT^A^J/, bisect its sides and draw the square 11, 12, 



46 



MECHANICAL DRAWING. 



13, 14. Draw the diagonals 11, 13 and 12, 14 and divide 
them as shown in Drawing No. 2. At the intersections of 
the horizontal with the perpendicular full lines locate the 
points I, 2, 3, 4, etc., which will be the centers of the quad- 
rants of the outer curve. The centers for the inner curve 
will be found at the intersections of the horizontal and per- 




FiG. 77. 
pendicular broken lines, drawn through the divisions on the 
diagonals. Then with center i and radius iPdraw arc PiV, 
and with center 2 and radius 2N draw arc NM, with center 3 
and radius 3^1/ draw arc ML, etc. The inner curve is drawn 
in a similar way, by using the points on the diagonals indi- 
cated by the broken lines as centers. 

Fig. 78. To Describe the Cycloid. — AB is the di- 
rector, CB the generating circle, Jf a piece of thin transparent 
celluloid, with one side dull on which to draw the circle C. 
At any point on the circle C puncture a small hole with a 
sharp needle, and place the point C tangent to the director 
AB at the point from which the curve is to be drawn. Hold 
the celluloid at this point with a needle, and rotate it until 



GEOMETRICAL DRAWING. 



47 



the arc of the circle C intersects the director AB. Through 
the point of intersection stick another needle and rotate X 
until the circle is again tangent to AB, and through the punc- 
ture at C with a 4H pencil, sharpened to a fine conical point, 
mark the first point on the curve. So proceed until sufficient 
points have been found to complete the curve. 

(Note. — The thin celluloid was first used as a drawing 
instrument by Professor H. D. Williams, of Sibley College, 
Cornell University.) 

Fig. 79. To Find the Length of a Given Arc of a 
Circle approximately. — Let BC be the given arc. Draw 
its chord and produce it to A, making BA equal half the 



/V 


v^^ - 


G 


/) 


V 




A 




'B 




Fig. 78. 



Fig. 79. 



chord. With center^ and radius ^4(7 describe arc crZ> cut- 
ting the tangent line BD at D, and making it equal to the 
arc BC. 

Fig. 80. To Describe the Cycloid by the Old 
IMethod. — Divide the director and the generating circle into 
the same number of equal parts. Through the center a draw 
ag parallel to AB for the line of centers, and divide it as AB 
in the points/', c, d, e,f, and ^. With centers/, e, d, etc., de- 
scribe arcs tangent to AB, and through the points of division 
on the generating circle 1,2, 3, etc., draw lines parallel to 



48 



MECHANICAL DRA WING. 



AB cutting the arcs in the points i', 2' , 3', etc. These will be 
points in the curve. 

An approximate curve may be drawn by arcs of circles. 
Thus, taking/"^ as center and f g' as radius, draw arc g' i' ^ 




Fig. 80. 



Produce \'f' and 2V until they meet at the center of the 
second arc 2'f\ etc. 

Fig. 81. To Describe the Epicycloid and the 
Hypocycloid. — Divide the generating circle into any num- 
ber of equal parts, i, 2, 3, etc., and set off these lengths from 
C on the directing circle CB as e' , d' , c' , etc. From A the cen- 
ter of the directing circle draw lines through e\ d' , c' , etc., cut- 
ting the circles of centers in e, d, c, etc. From each of these 
points as centers describe arcs tangent to the directing circle. 
From center A draw arcs through the points of division on 
the generating circle, cutting the arcs of the generating circles 
in their several positions at the points i', 2' , 3^ etc. These 
will be points in the curve. 

Fig. 82. Another Method. — Draw the generating 
circle on the celluloid and roll it on the outside of the gener- 
ating circle BC for the Epicycloid, and on the inside for the 



GEOMETRICAL DRAJVIXG. 



49 



Hypocycloid, marking the points in the curve 1,2, 3, etc., in 
similar manner to that described for the Cycloid. 

Fig. 82. 




Fig. 83. 



Fig. 83. To Draw the Cissoid. — Draw any line AB 
and BC perpendicular to it. On BC describe a circle. From 
the extremity C of the diameter draw any number of lines, 
at any distance apart, passing through the circle and meeting 
the line AB in i' , 2', 3', etc. Take the length from ^ to 9 
and set it off from C on the same line to g" . Take the dis- 
tance from 8' to 8 and set it off from C on the same line to 
8", etc., for the other divisions, and through 9", 8'', y" , 6", 
etc., draw the curve. 



50 



MECHANICAL DRA WING. 



Fig. 84. To Draw Schiele's Anti-friction Curve. 
— Let AB be the radius of the shaft and ^i, 2, 3, 4, etc., its 
axis. Set off the radius AB on the straight edge of a piece 
of stiff paper or thin celluloid and placing the point B on the 
division i of the axis, draw through points the line A\. 
Then lower the straight edge until the point B coincides with 
2 and the point y4 just touches the last line drawn, and draw 
a2, and so proceed to find the points a, b, c, etc. Through 
these points draw the curve. 




4 6 




Fig. 84. 



Fig. 85. 



Fig. 85. To Describe an Interior Epicycloid. — 
Let the large circle X be the generator and the small circle 
Y the director. Divide circle Y into any number of equal 
parts, as B, H, /, /, etc. Draw radial lines and make HCy 
ID, JE, KF, etc., each equal to the radius of the generator 
X. With centers C, D, E, etc., describe arcs tangent at 
H, I, J, etc. Make Hi equal to one of the divisions of the di- 
rector as BH. Make I2 equal to two divisions, ^3, three divi- 
sions, etc., and draw the curve through the points i, 2, 3, 4, 



GE OME TRIG A L DRA WING. 



51 



etc. This curve may also be described with a piece of cellu- 
loid in a similar way to that explained for the cycloid. 

It may not be out of place here to describe a few of the 



MOULDINGS USED IX ARCHITECTURAL WORK, 

since they are often found applied to mechanical constructions. 
Fig. 86. To Describe the "Scotia." — i, i is the top 
line and 4, 4 the bottom line. From i drop a perpendicular 
I, 4; divide this into three equal parts, as i, 2, and 3. 
Through the point 2 draw ab parallel to I, i. With center 2 
and radius 2, i describe the semicircle alb, and with center b 
and radius ba describe the arc ^5 tangent to 4, 4 at 5, draw 
the fillets I, I and 4, 4. 





i 


A 


:\ 


Q 


3 

. 5 


L J, 1 




Fig. 86. 



Fig. S7. 



Fig. 8;. To Describe the " Cyma Recta." — Join i, 
3 and divide it into five equal parts, bisect i, 2 and 2, 3, and 
with radius equal to i, 2 and 2, 3 respectively describe arcs 
I, 2 and 2,3. Draw the fillets i, i and 3, 3 and complete the 
moulding. 

Fig. 88. To Describe the "Cavetto" or "Hol- 
low." — Divide the perpendicular i, 2 into three equal parts 
and make 2, 3 equal to two of these. From centers i and 3 
with a radius somewhat greater than the half of i, 3, describe 
arcs intersecting at the center of the arc i, 3, 



52 



MECHANICAL DRAWING. 



Fig. 89. To Describe the *' Echinus, '^ ''Quarter 
Round," or "Ovolo." — Draw i, 2 perpendicular to 2, 3, 
and divide it into three equal parts. Make 2, 3 equal to 
two of these parts. From the points 2 and 3 with a radius 
greater than half 1,3, describe arcs cutting in the center of 
the required curve. 




Fig. 90. To Describe the "Apophygee." — Divide 
3, 4 into four equal parts and lay off five of these parts from 
3 to 2. From points 2 and 4 as centers and radius equal to 
2,3, describe arcs intersecting in the center of the curve. 





Fig. 90. 

Fig. 91. To Describe the ''Cyma Reversa." — Make 
4, 3 = 4, I. Join I, 3 and bisect it in the point 2. From the 
points I, 2 and 3 as centers and radii equal to about two-thirds 
of 1 , 2 draw arcs intersecting at 5 and 6. Points 5 and 6 
are the centers of the reverse curves. 

Fig. 92. To Describe the '' Torus." — Let i, 2 be the 
breadth. Drop the perpendicular i, 2, and bisect it in the 



GEOMETRICAL DRAWIXG. 



53 



point 3. With 3 as center and radius 3, i, describe the semi- 
circle. Draw the fillets. 




Fig. 92. 




Fig. 93. 



Fig. 93. An Arched Window Opening. — The curves 
are all arcs of circles, drawn from the three points of the equi- 
lateral triangle, as shown in the figure. 

Fig. 94. To Describe the ''Trefoil." — The equi- 
lateral triangle is drawn first, and the angle 1,2,3 bisected by 
the line 2, 4, which also cuts the perpendicular line i, 6in the 
point 6. The center of the surrounding circles i, 2 and 3 are 
the centers of the trefoil curves. 

Fig. 95. To Describe the ''Quatre Foil." — Draw 
the square i, 2, 3, 4 in the position shown in the figure. The 
center of the surrounding circles, point 5, is at the intersection 
of the diagonals of the square. Points i, 2, 3, 4 of the square 
are the centers of the small arcs. 

Fig. 96. To Describe the " Cinquefoil Orna- 
ment." The curves of the cinquefoil are described from the 
corners of a pentagon i, 2, 3, 4, 5. Bisect 4, 5 in 6 and draw 
2, 6, cutting the perpendicular in the point 7, the center of 
the large circles. 

Fig. 97. To Draw a Baluster. — Begin by drawing 
the center line, and lay off the extreme perpendicular height, 



54 



MECHAXICAL DRAWING. 



the intermediate, perpendicular, and horizontal dimensions, 
and finally the curves as shown in the figure. 



Fig. 94. 



Fig. 95. 



Fig. 96. 




Fig. 97. 



DRAWING TO SCALE. 

When we speak of a drawing as having been made to scale, 
we mean that every part of it has been drawn proportionately 
and accurately, Q\th.Qr full sice, reduced or enlarged. 

Very small and complicated details of machinery are usu- 
ally drawn enlarged ; larger details and small machines may 
be made full size, while larger machines and large details are 
shown reduced. 

When a drawing of a machine is made to a reduced or en- 
larged scale the figures placed upon it should ahvays give the 
full-size dimensions, i.e., the sizes the machine should meas- 
ure when finished. 



GEOMETRICAL DRAWING. 



55 



Fig. 98. To Construct a Scale of Third Size or 
A^'=- I Foot. — Draw upon a piece of tough white drawing- 
paper two parallel lines about \" apart and about 14'' long as 
shown by a, Fig. 98. From A lay off distances equal to 4" 
and divide the first space AB into 12 equal parts or inches by 
Prob. 12. Divide AB'm the same way into as many parts as 

it may be desired to subdivide the inch divisions on AB, 
E 






u 


.<>• a- 




V 


n' r 






jr 10- 


8- 7- 


,r Jf- 




2' 1' 




Scale 


/= 


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b 






















































































1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 






ill 


III 


ill 


ill 


ill 


II 


ill 


ill 


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ill 


ill 


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Fig. gS. 

usually 8. When the divisions and subdivisions have been 
carefully and lightly drawn in pencil, as shown by a, in Fig. 
98, then the lines denoting i'\i'\ i'\ i" , and 3'' should be 
carefully inked and numbered as shown by {b). By a further 
subdivision a scale of 2''= i foot may easily be made as shown 
by {c) in Fig. 98. 



CHAPTER III. 
CONVENTIONS. 

It is often unnecessary if not undesirable to represent cer- 
tain things as they would actually appear in a drawing, espe- 
cially when much time and labor is required to make them 
orthographically true. 

So for economic reasons draftsmen have agreed upon con- 
ventional methods to represent many things that would other- 
wise entail much extra labor and expense, and serve no par- 
ticular purpose. 

It is very necessary, however, that all draftsmen should 
know lioiv to draw these things correctly, for occasions will 
often arise when such knowledge will be demanded ; and be- 
sides it gives one a feeling of greater satisfaction when using 
conventional methods to know that he could make them artis- 
tically true if it was deemed necessary. 

STANDARD CONVENTIONAL SECTION LINES. 

Conventional section lines are placed on drawings to distin- 
guish the different kinds of materials used when such drawings 
are to be finished in pencil, or traced for blue printing, or to 
be used for a reproduction of any kind. 

Water-colors are nearly always used for finished drawings 

and sometimes for tracings and pencil drawings. 

The color tints can be applied in much less time than it 

56 



CONVENTIONS. 57 

takes to hatch-line a drawing. So that the color method 
should be used whenever possible. 

Fig. 99. — This figure shows a collection of hatch-lined 
sections that is now the almost universal practice among 
draftsmen in this and other countries, and may be considered 
standard. 

No. I. To the right is shown a section of a wall made of 
rocks. When used without color, as in tracing for printing, 
the rocks are simply shaded with India ink and a 175 Gillott 
steel pen. For a colored drawing the ground work is made 
of gamboge or burnt umber. To the left is the conventional 
representation of water for tracings. For colored drawings 
a blended wash of Prussian blue is added. 

No. 2. Convention for Marble. — When colored, the 
whole section is made thoroughly wet and each stone is then 
streaked with Payne's gray. 

No. 3. Convention for Cliestnnt. — When colored, a 
ground wash of gamboge with a little crimson lake and burnt 
umber is used. The colors for graining should be mixed in a 
separate dish, burnt umber with a little Payne's gray and 
crimson lake added in equal quantities and made dark enough 
to form a sufficient contrast to the ground color. 

No. 4. General Convention for Wood. — When colored the 
ground work should be made with a light wash of burnt sienna. 
The graining should be done with a writing-pen and a dark 
mixture of burnt sienna and a modicum of India ink. 

No. 5. Convention for Black Walnut. — A mixture of 
Payne's gray, burnt umber and crimson lake in equal quanti- 
ties is used for the ground color. The same mixture is used 
for graining when made dark by adding more burnt umber. 



58 



MECHANICAL DRAWING. 




CONVEX TIOXS. 59* 

No. 6. Convention for Hard Pine, — For the ground 
color make a light wash of crimson lake, burnt umber, and 
gamboge, equal parts. For graining use a darker mixture of 
of crimson lake and burnt umber. 

No. 7. Convention for Building- stone. — The ground 
color is a light wash of Payne's gray and the shade lines are 
added mechanically with the drawing-pen or free-hand with 
the writing-pen. 

No. 8. Convention for EartJi. — Ground color, India ink 
and neutral tint. The irregular lines to be added with a writ- 
ing-pen and India ink. 

No. 9. Section Lining for Wrought or Malleable Iron. — 
When the drawing is to be tinted, the color used is Prussian 
blue. 

No. 10. Cast Iron. — These section lines should be drawn 
equidistant, not very far apart and narrower than the body 
lines of the drawing. The tint is Payne's gray. 

No. : I. Steel. — This section is used for all kinds of steel. 
The lines should be of the same width as those used for cast- 
iron and the spaces between the double and single lines should 
be uniform. The color tint is Prussian blue with enough crim- 
son lake added to make a warm purple. 

No. 12. Brass. — This section is generally used for all 
kinds of composition brass, such as gun-metal, yellow metal, 
bronze metal, Muntz metal, etc. The width of the full lines, 
dash lines and spaces should all be uniform. The color tint 
is a light wash of gamboge. 

Nos. 13-20. — The section lines and color tints for these 
numbers are so plainly given in the figure that further instruc- 
tion would seem to be superfluous. 



6o MECHANICAL DRAWING, 

CONVENTIONAL LINES. 

Fig. 100. — There are four kinds: 

(i) The Hidden Line. — This Hne should be made of short 
dashes of uniform length and width, both depending some- 
what on the size of the drawing. The width should always 
be slii^htlv less than the body lines of the drawing, and the 

(■ 

length of the dash should never exceed \" . The spaces 
between the dashes should all be uniform, quite small, never 
exceeding yV''- This line is always inked in with black ink. 

(2) TJie Line of JMotion. — This line is used to indicate 
point paths. The dashes should be made shorter than those of 
the hidden line, just a trifle longer than dots. The spaces 
should of course be short and uniform. 

(3) Center Lines. — Most drawings of machines and parts 
of machines are symmetrical about their center lines. When 
penciling a drawing these lines may be drawn continuous and 
as fine as possible, but on drawings for reproductions the black- 
inked line should be a long narrow dash and two short ones 
alternately. When colored inks are used the center line should 
be made a continuous red line and as fine as it is possible to 
make it. 

(4) Dimension Lines and Line of Seetion. — These lines 
are made in black with a fine long dash and one short dash 
alternately. In color they should be continuous blue lines. 



CONVENTIONS. 



61 



Colored lines should be used wherever feasible, because they 
are so quickly drawn and when made fine they give the drawing- 
a much neater appearance than when the conventional black 
lines are used. Colored lines should never be broken. 



CONVENTIONAL BREAKS. 

Fig. ioi. — Breaks are used in drawings sometimes to indi- 
cate that the thing is actually longer than it is drawn, some- 



BS^ 



£sS9 



l k^.^.^^.^^'.^^.^^^^ ■ ^'^'.^■^^■■^^^^^^^^^^^ 



^.^^.^^^^^^^^^■^^■^^^^^^^^^^<^^^^^^^^^^.vy 



Fig. ioi. 



times to show the shape of the cross-section and the kind of 
material. Those given in Fig. loi show the usual practice. 



CROSS-SECTIONS. 

Fig. 102. — When a cross-section of a pulley, gear-wheel 
or other similar object is required and the cutting-plane passes 
through one of the spokes or arms, then only the rim and hub 
should be sectioned, as shown at xx No. i and zz No. 2, and 
the arm or spoke simply outlined. Cross-sections of the arms 
may be made as shown at A A No. 2. In working drawings of 



62 



MECHANICAL DRAWING. 



gear-wheels only the number of teeth included in one quadrant 
need be drawn ; the balance is usually shown by conventional 
lines, e.g., t\\Q pitch line the same as a center line, viz., a long 




Fig. I02. 

dash and two very short ones alternately or a fine continuous 
red line. 

The addeiidmn line {d) and the root or bottom line {U) the 
same as a dimension line, viz., one long dash and one short 
dash alternately or a fine continuous blue line. The end ele- 
vation of the gear-teeth should be made by projecting only 
the points of the teeth, as shown at No. 2. 

CONVENTIONAL METHODS OF SHOWING SCREW-THREADS IN 
WORKING DRAWINGS. 



Fig. 103. — No. i, shows the convention for a double 
V thread, U. S. standard; No. 2, a single V thread; No. 3, 
a single square thread; No. 4, a double left-hand V thread; 
No. 5, a double right-hand square thread; No. 6, any 
thread of small diameter; No. 7, any thread of very small 
diameter. The true methods for constructing these threads 
are explained on pages 99-101, Figs. 99-101. 

In No. 6. the short wide line is equal to the diameter 
of the thread at the bottom. The distance between the 



COXVENTIO.XS. 



63 



longer narrow lines is equal to the pitch, and the inclination 
is equal to half the pitch. 

The short dash lines in No. 7 should be made to corre- 




=r 



J^ ^-^ 



Fig. 103. 

spond to the diameter of the thread at the bottom. After 
some practice these lines can be drawn accurately enough by 
the eye. 



CHAPTER IV. 
LETTERING AND FIGURING. 

This subject has not been given the importance it deserves 
in connection with mechanical drawing. Many otherwise ex- 
cellent drawings and designs as far as their general appearance 
is concerned have been spoiled by poor lettering and figuring. 

All lettering on mechanical drawings should be plain and 
legible, but the letters in a title or the figures on a drawing 
should never be so large as to make them appear more prom- 
inent than the drawing itself. 

The best form of letter for practical use is that which gives 
the neatest appearance with a maximum of legibility and re- 
quires the least amount of time and labor in its construction. 

This would naturally suggest a " free-hand " letter, but be- 
fore a letter can be constructed '' free-hand " with any degree 
of efficiency, it will be necessary to spend considerable time 
in acquiring a knowledge of the form and proportions of the 
particular letter selected. 

It is very desirable then that after the student has care- 
fully constructed as many of the following plates of letters and 
numbers as time will permit and has acquired a sufficient 
knowledge of the form and proportions of at least the " Ro- 
man " and " Gothic" letters; he should then adopt some one 

64 



LETTERING AND FIGURING. 65 

|l style and practice that at every opportunity, until he has at- 
tained some proficiency in its free-hand construction. 

When practicing the making of letters and numbers free- 
hand, they should be made quite large at first so as to train 
the hand. 

The " Roman " is the most legible letter and has the best 
appearance, but is also the most difficult to make well, either 
free-hand or mechanically. However, the methods given for 
its mechanical construction. Figs. 104 and 105, will materially 
modify the objections to its adoption for lettering mechanical 
drawings. 

The ''Gothic" letter is a favorite with mechanical drafts- 
men, because it is plain and neat and comparatively easy to 
construct. (See Fig. 106.) 

Among the type specimens given in the following pages 
the Bold-face Roman Italic on page 70 is one of the best 
for a good, plain, clear, free-hand letter, and is often used 
with good success on working drawings. Gillott's No. 303 
steel pen is the best to use when making this letter free-hand. 

The " Yonkers " is a style of letter that is sometimes 
used for mechanical drawings. It is easy to construct with 
either F. Soennecken's Round Writing-pens, single point, or 
the Automatic Shading-pen. But it lacks legibility, and is 
therefore not a universal favorite. 

A good style for " Notes" on a drawing is the " Gothic 
Condensed " shown on page 70. 

When making notes on a drawing with this letter, the. 
only guides necessary are two parallel lines, drawn lightly in 
pencil. The letters should be sketched Hghtly in pencil firsts 



^6 MECHANICAL DRAWING. 

and then carefully inked, improving spacing and proportions 
to satisfy the practiced eye. 

FIGURING. 

Great care should be taken in figuring or dimensioning a 
mechanical drawing, and especially a working drawing. 

To have a drawing accurately, legibly, and neatly figured 
is considered by practical men to be the most important part 
of a working drawing. 

There should be absolutely no doubt whatever about the 
character of a number representing a dimension on a drawing. 

Many mistakes have been made, incurring loss in time, 
labor, and money through a wrong reading of a dimension. 

Drawings should be so fully dimensioned that there will 
be no need for the pattern-maker or machinist to measure any 
part of them. Indeed, means are taken to prevent him from 
doing so, because of the liability of the workman to make 
mistakes, so drawings are often made to scales which are dif- 
ficult to measure with a common rule, such as 2 "and 4'^ = 
I ft. 

The following books, among the best of their kind, are 
recommended to all who desire to pursue further the study 
of '' Lettering" : Plain Lettering, by Prof. Henry S. Jacoby, 
Cornell University, Ithaca, N. Y. ; Lettering, by Charles W. 
Reinhardt, Chief Draftsman, Engineering News, New York; 
Free-hand Lettering, by F. T. Daniels, instructor in C. E. in 
Tufts College. 



LETTERIXG AND FICURIXG. 



67 



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ME CHA NIC A L BRA IVIXG. 



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LETTERING AND FIGURING. 



6g 




70 MECHANICAL DRAWIXG, 



iS-Point Roman. 



ABCDEFGHIJKLM^^ OPQRSTUYAYX 
YZ abcdefgliijklmnopqrstuvwxyz 
1234567890 



iS-Point Italic. 



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17- Point Gushing Italic. 

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nopqrstuvwxyz 1234567890 

28-Point Boldface Italic. 

ABCDEFGHIJKL3I 
NOPQRSTUVWXYZ 

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Two-Line Nonpareil Gothic Gondensed. 

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Three-Line Nonpareil Lightface Celtic. 

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LETTERING AND FIGURING. 7 1 



i8-Point Chelsea Circular. 



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iS-roint Elandkay. 

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iS-Point Quaint Open. 

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28-Point Roman. 

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28-Point Old-Style Italic. 



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i2-Point Victoria Italic. 

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iS-Point DeVinne Italic. 

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22-Point Gothic Italic. 

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Double-Pica Program. 



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Nonpareil Telescopic Gothic. 

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LETTERIXG AXD FIGURING. 73 



-Point Gallican. 



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Two-Line Virile Open. 



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22-Point Old-Stvle Roman. 



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36-Point Yonkers. 




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CHAPTER V. 
ORTHOGRAPHIC PROJECTION. 

Orthographic Projection, sometimes called Descrip- 
tive Geometry and sometimes simply Projection, is one of 
the divisions of descriptive geometry; the other divisions are 
Spherical Projection, Isometric Projection, Shades and 
Shadows, and Linear Perspective. 

In this course we will take up only a sufficient number of 
the essential principles of Orthographic Projection, Isometric 
Projection, and Shades and Shade Lines, to enable the stu- 
dent to make a correct mechanical drawing of a machine or 
other object. 

Orthographic Projection is the science and the art of rep- 
resenting objects on different planes at right angles to each 
other, by projecting lines from t\\Q povit of sight through the 
principal points of the object perpendicular to the Planes of 
Projection. 

There are commonly three planes of projection used, viz., 
the H. P. or Horizontal Plane, the V. P. or Vertical PlaiiCy 
and the Pf. P. or Profile Plane. 

These planes, as will be seen by Figs. 107 and 109, inter- 
sect each other in a line called the /. L. or Intersecting Line, 
and form four angles, known as the first, second, third, and 

74 



GR THO GRA PHIC PR OJE C TIGX. 



75 



fourth DiJicdral Angles. Figs. 107 and 109 are perspective 
views of these angles. 

An object may be situated in any one of the dihedral 
angles, and its projections drawn on the corresponding co- 
ordinate planes. 

Problems in Descriptive Geometry are usually worked out 
in the first angle, and nearly all English draftsmen project 
their drawings in that angle, but in the United States the 
third angle is used almost exclusively. There is good reason 
for doing so, as will be shown hereafter. 

We will consider first a few projection problems in the 
first angle, after which the third angle will be used throughout. 




Fig. 107. 

H.P., Fig. 107, is the Horizontal Plane, V.P. the Vertical 
Plane, and I.L. the Intersecting Line. 

The Horizontal Projection of a point is where a perpen- 
dicular line drawn through the point pierces the H.P. 

The Vertical Projection of a point is where a per. line 
drawn through the point pierces the V.P. 

Conceive the point a, Fig. 107, to be situated in space ^' 
above the H.P. and 3" in front of the V.P. If a line is 
passed through the point a per. to H.P. and produced until 



76 MECHANICAL DRAWING. 

it pierces the H.P. in the point a}\ <^^'will be the Hor. Proj. 
of the point a. 

If another Hne is projected through the point a per. to the 
V.P. until it pierces the V.P. in the point a", a" is the ver- 
tical projection of the point a. 

If now the V.P. is revolved upon its axis I.L. in the di- 
rection of the arrow until it coincides with the H.P. and let 
the H.P. be conceived to coincide with the plane of the 
drawing-paper, the projections of the point a will appear as 
shown by Fig. io8. 

The vertical projection a" 4" above the I.L. and the 
horizontal projection a^' i" below the I.L. both in the same 
straight line. 

In mechanical drawing the vertical projection a" is called 
the Elevation and the horizontal projection a!' the Plan. 

The projections of a line are found in a similar manner, 
by first finding Ihe projections of the two ends of the line, 
and joining them with a straight line. 

Let ab be a line in space 32'^ long, parallel to the V.P. 
and perpendicular to the H.P. One end is resting on the 
H.P. 2^" from the V.P. 

The points a and b will be vertically projected in the 
points <?" and b'" , Join a'^b'". a'"b'" is the vertical projection of 
the line ab. 

When a line is perpendicular to one of the planes of pro- 
jection, its projection on that plane is a point, and the projec- 
tion on the other plane is a line equal to the line itself. 

ab, Fig. 107, is perpendicular to the H.P., therefore its 
proj. on the H.P. when viewed in the direction <^<^'will be 
seen to be a point. 



ORTHOGRAPHIC PROJECTION. 



)7 



Conceive now the V.P. revolved as before, the V. proj. 
will be found to be at d"b"^ Fig. io8, and the H. proj. at the 
point a!\ 

cdy Fig. 107, is a line parallel to the H.P. and perpendic- 
ular to the V.P. Its elevation or V. proj. is the point d^\ Fig. 
108, and its plan or H. proj. the line c^'d'' perpendicular to 
the Intersecting Line and equal in size to the line itself. 

Planes or Plane Surfaces bounded by lines are projected 
by the same principles used to project lines and points. 

Let aa''-'b''b, Fig. 107, be a plane at right angles to and 
touching both planes of projection. 

The elevation of the front upper corner a is projected in 
the point a". The elevation of the front lower corner b is pro- 
jected in the point b"". Join d^'b'". d'b'" is the vertical projection 
of the front edge ab of the plane. The plan of the front 



y 

^ d T 

I ^ 

_L_-i^ 

c 

d a 



Fig. ioS, 

upper corner is projected in the point b and the point a" in the 
point b". A straight line joining bb"" is the plan or horizontal 
projection of the top edge of the plane. 

On the drawing-paper the plan and elevation of the plane 
aa^b a would be shown as a continuous straight line a" to a!" 
Fig. 108. 



78 



MECHAXICAL DRA IVIA G. 



Solids bounded by plane surfaces are projected by means 
of the same principles used to project planes, lines, and points. 

C, Fig. 107, is a cube bounded by six equal sides or sur- 
faces. The top and bottom being parallel to the H.P. and 
the front and back parallel to the V.P., the vert. proj. is a 
square above I.L. equal in area to any one of the six faces 
of the cube. The hor. proj. is a similar square below I.L. 

These projections are shown at C, Fig. 108, as they would 
appear on the drawing-paper. 

The foregoing illustrates a few of the simple principles of 
projection in relation to points, lines, and solids when placed 
in the first dihedral angle, and we find that the plan is always 
below and the elevation always above the I.L. 

Let us now consider the same problems when situated in 
the //22><3^ angle. The point <3r, Fig. 109, is behind^ the V.P. 




Fig. 109. 



and below the H.P. Draw through a perpendiculars to the 
plane of projection. The Hor. proj. is found at a^ and the 
vert. proj. at d^ , 

Conceive again the V.P. to be revolved in the direction 
of the arrow until it coincides with the H. P. The hor. proj. 



OR THO GRA PHIC PR OJE C TION, 



79 



will then appear at a'' above the I.L. and the vert. proj. at a" 
beloiv the I.L., Fig. no. And so with the lines, the planes, 
and the solids. 



T I c 


T j' 


c 








r> 






. '^ 


1 


o- a- 



Fig. no. 



In order to still further explain _the use of the planes of 
projection, with regard to objects placed in the third angle, 
let us suppose a truncated pyramid surrounded by imaginary 
planes at right angles to each other, as shown by Fig. in. 




Fig. III. 

With a little attention it will easily be discerned that the 
pyramid is situated in the third dihedral angle, and that in 
addition to the V. and H. planes, we have passed two profile 
planes at right angles to the V. and H. planes, one at the right- 
hand and one at the left. 

When the pyramid is viewed orthographically through 
each of the surrounding planes, four separate views are had, 



8o 



MECHANICAL BRA WIA'G. 



exactly as shown by the projections on the opposite planes, 
viz., a Front View, Elevation, or Vert. Proj. at F. ; a Right- 
hand View, Right-end Elevation, or Right-profile Projection 
at R. ; a Left-hand View, Left-end Elevation, or Left-profile 
Projection at L. ; a Top View, Plan or H. Proj. at P. 

If we now consider the V.P. and the right and left profile 
planes to be revolved toward the beholder until they coincide, 
using the front intersecting lines as axes, the projections of the 
pyramid will be seen as shown by Fi»g. 112, which when the 



/ // 


-^^'^ 


p 


"""^"""^ 


$x 


.^^^^ 




\ / 




^^^^-^ 


^^^"^ 






I 






~"^^~^\ 


/""'^ 




/ 




\ 




~~"^\ 




(( 


( 


Y 












^ 


\ 


V 


\ 




























\ 




1 


\ 






I 




\ 






/ 


. 


L 


F 


R 





Fig. 112. 

imaginary planes and projecting lines have been removed, will 
be a True Drawing or Orthographic Projection of the truncated 
pyramid. 

NOTATION. 



In the drawings illustrating the following problems and 
their solutions the giveyi and required lines are shown wide and 
black. Hiddcii lines are shown broken into short dashes a little 
narrower than the visible lines. Construction ox projection lines 
are drawn with very narrow full or coiitijiuous black lines. 



ORTHOGRAPHIC PROJECTION. 8 1 

When convenient very narrow, continuous blue lines are some- 
times used. 

The Horizontal Plane is known as the H.P., the Vertical 
Plane as V.P. and the Profile Plane as Pf.P. 

A point in space is designated by a small letter or figure, 
their projection by the same letters or figures with small Ji or 
V written above for the horizontal or vertical projection re- 
specti\-ely. 

In some complicated problems where points are designated 
by figures their projections are named by the same figures 
accented. 

Drawings should be carefully made to the dimensions 
given, the scale to be determined by the instructor. 

The student should continually endeavor to improve in 
inking straight lines, curves, and joints. 

In solving the following problems the student should have 
a model of the co-ordinate planes for his own use. This can 
be made by taking two pieces of stiff cardboard and cutting a 
slot in the center of one of them large enough to pass the 
folded half of the other through it ; when unfolding this half a 
model will be had like that shown by Fig. 107 or 109. 

All projections shall now be made from the third, 
dihedral angle. 

Prob. I. — A point a is situated in the third dihedral 
angle, i'' below the H.P. and 3" behind the V.P. 

It is required to draw its vertical and horizontal projec- 
tions. 

Draw a straight line a!'d% Fig. 113, perpendicular to I.L. 
and measure off the point a" \" below I.L. and the point a!'- 
3" above I.L. 



82 



MECHANICAL DRAWING. 



(f is the vertical and a!' the horizontal projection in the 
same straight line cCa!'. 

The student should demonstrate this with his model. 

Prob. 2. — Draw two projections of a line 3'Mong parallel 
to both planes, |" below the H.P. and 2" behind the V.P. 

As the line is parallel to both planes, both projections will 
be parallel to the I.L. 

Draw d^b'' the vert. proj. of the line i" long, Fig. 1 14, par- 
allel to I.L. and f" below it. Draw the hor. proj. 2" above 
the I.L. and parallel to it, making it the same length as the 





a 

c 






h 

/ 


\ " 






b 


*; 




b 


K 


/ 




\ ^ 












\ 


^^ 1 






a 


y 


a 






T 




a 










a.] 




a 




bt 




i" 




b" 




^<^ i 








a 


2." 


h 


"^^^ 


1/ 



Fig. 113, Fig. 114. Fig. 115. Fig. 116. Fig. 117. 

vert. proj. by drawing lines perpendicular to I.L. from the 
points a" and b"" to a^' and b^\ 

Prob. 3. — To draw the hor. and vert, projs. of a straight 
line 3'' long, per. to the vert, plane. Fig. 115. 

As the line is per. to the vert, plane the vert. proj. will be 
a point below the I.L. and the hor. proj. will be parallel to 
the horizontal plane and per. to I.L. 

Prob. 4. — To draw the plan and elevation of a straight 
line 6" long making an angle of 41;° with the vert, plane and 
and par. to the hor. plane, Fig. 116. 



ORTHOGRAPHIC PROJECTION. Z^ 

The plan or hor. proj. will be above the I.L. and make an 
angle of 45° with it. The elevation or vert. proj. will be 
below and par. to I.L. 

Draw from the point a'' at any convenient distance from 
I.L. a straight line cd'U' 6" long, making an angle 45° with I.L. 

Draw a^b" par. to I.L= at a convenient distance below it. 
The length of the elevation or vert. proj. is determined by 
dropping perpendiculars from the end of the hor. proj. a'^b^' to 
the points a"b'\ 

PrOB. 5, Fig. 117. — To find the true length of a straight 
line oblique to both planes of projection and the angle it 
makes with these planes. 

a^b"" and a''b^' are the projections of a straight line oblique 
to V.P. and H.P. Using a" as a pivot, revolve the line a"b'" 
until it becomes parallel to I.L. as shown by a'"b^''. From the 
point ^^i" erect a per. Through the point b^' draw a line par. to 
I.L. cutting the per. in the point b^'. 

^ The broken line a^'b^' \s the true length of the line ^<^, 
and the angle is the true angle which the line makes with 
V.P. 

To find the angle it makes with H.P, : 

Using b^' as a pivot, revolve the line ^V' until it becomes 
par. to I.L. as shown by b^'a^^. From the point rt:/' drop a per. 
Through the point a" draw a line par. to I.L. intersecting the 
per. at the point a^'o is the angle which the line ab makes 
with H.P. and the broken line a^'b" is again its true length. 

Prob. 6, Fig. 118. — To project a plane surface of given 
size, situated in the third angle and par. to the V.P. 

Let abed be the plane surface 3'' long X 2" wide. If 
wx conceive lines to be projected from the four corners of the 



84 MECHANICAL DRAWING. 

plane surface to theV.P. and join them with straight hnes we 
will have its V. projection a"' b'' c"' d'' and shown by Fig. ii8. 
And as the plane surface is par. to the V.P. it must be per 
to the H.P. since the planes of projection are at right angles 
to each other. So the plan or H. projection will be a straight 
line equal in length to one of the sides of the plane surface. 

At a convenient distance above I.L. draw a straight line, 
and from the points ^"^^"^ project lines at right angles to I.L., 
cutting the straight line in the points a^'b} The line a!'b^' is 
the hor. proj. of the plane surface abed. 

Prob. 7, Fig. ii8. — To draw the projections of a plane 
surface of given dimensions when situated in the third angle 
perpendicular to the H.P. and making an angle with the V.P. 

Let the plane surface be 3" X 2'' as before and let the 
angle it makes with V.P. be 60°. 

To draw the plan : 

At a convenient distance above I.L. and makincr an ano-le 
of 60° with it, draw aJ'bl\ Fig. 1 18, 2" long. From b^' drop a 
per. cutting d'b"' in the point b~' and t'd'' in the point d^\ then 
the rectangle d'b^'d^'c' will be the vert. proj. or elevation of 
the plane surface abed. 

Prob. 8, Fig. 119. — To draw the projections of the same 
plane surface (i) when parallel to the H.P., (2) when making 
an angle of 30° with H.P. and per. to V.P., (3) when mak- 
ing an angle of 60° with H.P. and per. to V.P., and (4) when 
per. to both planes. 

Fig. 119 shows the projections; further explanations are 
unnecessary. 

Prob. 9, Figs. 119 and 120. — To draw the projections of 



ORTHCGRAPHIC PROJECTION 



85 



the same plane surface when making compound angles with 
the planes of projection. 

Let the plane make an angle of 30° with H.P., as in the 
second position of Prob. 8, Fig. 119, and in addition to that, 
revolve it through at angle of 30°. First, draw the plane 
parallel to H.P., as shown by a''c''b'Ui^\ Fig. 119, the true size 
of the plane. 




r b, hj d} 

Fig. 118. Fig. iig. Fig. 120. 

Its elevation will be the straight line a'd'" parallel to I.L. 
Next revolve a"b'", using a" as a pivot, through an angle of 
30°, to the position a"b^\ which is its vert. proj. when making 
an angle of 30° with H.P. Its plan is projected in a^'bl'c''d^\ 

Now as the plane is still to make an angle of 30° with 
H.P. after it has been revolved through an angle of 30° with 
relation to the V.P., its hor. proj. will remain unchanged. 

With a piece of celluloid or tracing-paper trace the hor. 
proj. <^''3,Wj^, lettering the points as shown, and revolve the 



86 MECHANICAL DRA WING. 



tracing through the angle of 30°, or, which is the same things 
place the tracing so that the line a!'c^' will make an angle of 
60° with I.L., and with a sharp conical-pointed pencil trans- 
fer the four points to the drawing-paper and join them b}- 
straight lines, as shown by Fig. 120. 

And as the line d'c^' retains its position relative to H.P. 
after the revolution, its elevation will be found at cfc"^ Fig. 
120, in a straight line drawn through d"b'\ Fig. 119, intersect- 
ing perpendiculars from a!'d\ Fig. 120. And the vert. proj. 
of the points bl'dl' will be found at h^d^, Fig. 120, in a straight 
line drawn through b^, Fig. 119, parallel to I.L. and intersect- 
ing pers. from /^jV/', join with straight lines the points 
d"b,''c"d^. 

Draw the projections of the plane when making an angle 
of 60° wdth H.P. and revolved through an angle of 30° with 
relation to V.P. 

Draw the projections of the plane when making an angle 
of 60° with the V.P. and per. to the H.P., Fig. 120. 

Prob. 10. — To draw the projections of a plane surface of 
hexagonal form in the following positions: (i) When one 
of its diagonals is par. to the V.P. and making an angle of 
45° with the H.P. (2) When still making an angle of 45° 
with the H.P. the same diagonal has been revolved through 
an angle of 60^. 

Draw the hexagon i^'2''3V5''6'S Fig. 121, at any con- 
venient distance above I.L., making the inscribed circle 
= 2\" , This will be its hor. proj. and 2''4''6''i'' its vert, proj., 
the diagonal I ''2^' being par. to both planes of proj. With 
I'' as an axis revolve 6''4''2'' through an angle of 45°. Through 
the points 2j^4,^6/ erect pers. to the points 6/*5/'4/'3/' ^^i^ 2^ 



ORTHOGRAPHIC PROJECTION. 



87 



and join them with straight Hnes. These are the projs. in 
the first position. Now trace the hor. proj, i^', 2/', etc., on 
a piece of celluloid or tracing-paper and revolve the tracing 
until the diagonal i''2/' makes an angle of 60° with the I.L., 
Fig. 122. Next draw pers. from the 6 points of the hexag- 
onal plane to intersect hors. from the corresponding points of 
the elevation in Fig. 121, join the points of intersection with 




Fig. 121. Fig. 122. 

straight lines, and so complete the projections of the second 
position, Fig. 122. 

Prob. II, Figs. 123 and 124. — Draw the projs. of a cir- 
cular plane (i) when its surface is par. to the vert, plane, (2) 
when it makes an angle of 45° with the V.P., and (3) when 
still making an angle of 45° with the V.P. it has been re- 
volved through an angle of 60°. 

First position: Draw the circular plane i^', 2% 3^, 4^, etc., 
Fig. 123, below the I.L. with a radius = \^' and divide and 
figure it as shown. 



88 



ME CHA NIC A L DRA WING. 



Since the plane is par. to V.P. its hor. proj. will be a 
straight line i'\ 2^\ etc. 

For the second position revolve the said hor. proj. through 
the required angle 0(45° to the position cd' . . . . i^^, Fig. 123, 



and through each division 
a!' . . . , \^' in points 2^'f . . 



. . . . a!" draw arcs cutting 



. This is the hor. proj. of the 
plane when making an angle of 45° with the V.P. 

The elevation is found by dropping pers. from the points 
in the hor. proj. a!' . . ,\^ to intersect hor. lines drawn 
through the correspondingly numbered points in the eleva- 




FiG. 123. 



Fig. 124. 



tion and through these intersections draw the elevation or 
vert. proj. of the second position. 

For the third position make a tracing of the elevation of 
the second position, numbering all the points as before, and 
place the tracing so that the diameter 7^7" makes the required 
angle of 60° with the I.L. and transfer to the drawing-paper. 



ORTHOGRAPHIC PROJECTION. 89 

The result will be the elevation of the third position shown 
below the I.L., Fig. 124-. Its hor. proj. is found by drawing 
pers. through the points i, 2, 3,4 ... to intersect hors. drawn 
through the corresponding points in the hor. proj. of the 2d 
position and through these intersections draw the plan or hor. 
proj. of the third position, Fig. 124. 

Prob. 12, Fig. 125. — Draw the projs. of a regular hexag- 
onal prism, 3" high and having an inscribed circle of 4f" 
diam. : (i) When its axis is par. to the V.P. (2^ Draw the 
true form of a section of the prism when cut by a plane 
passing through it at an angle of 30"" with its base. (3) 
Draw the projection of a section when cut by a plane passing 
through XX, Fig. 125, per. to both planes of proj. 

The drawing of the I.L. may now be omitted. 

For the plan of the first part of this prob. draw a circle 
with a radius = to 2-f-^'\ and circumscribe a hexagon about it, 
as shown by a!'-, U\ U\ etc., Fig. 125. To project the elevation, 
draw at a convenient distance from the plan a hor. line par. 
to d'd\ and 3'' below it another line par. to it. From the 
points a!" y'' (^'- d''- , drop pers. cutting these par. lines in the points 
a''b''c''-'d'% thus completing the elevation of the prism. 

Second condition : Draw the edge view or trace of the 
cutting plane i'^' , making an angle of 30" with the base of the 
prism, locating the lower end 4' one-half inch above the base; 
parallel to i'^' , and at a convenient distance from it draw a 
straight line 1,4; at a distance of 2^^" on each side of 1,4 
draw lines 3, 2 and 5, 6 parallel to 1,4, and through the 
points i'2'3'4' let fall pers. cutting these three par. lines in 
the points i, 2, 3, 4, 5, 6; join these points by straight lines 



90 



MECHANICAL DRA WING, 



as shown, and a true drawing of the section of the prism as 
required will result. 

For the third condition of the problem : 

Let XX be the edge view of the cutting plane and con- 
ceive that part of the prism to the right of XX to be removed. 




Fig. 125. 



Fig. 126. 



From the hor. proj. of the prism draw a right-hand elevation 
or profile proj., and through the points XX draw the lines en- 
closing the section, and hatch-line it as shown. 

Prob. 13.— To draw the development of the lower part 
of the prism in the elevation of the last problem. 



ORTHOGRAPHIC PROJECTION. 9 1 

To the right of the elevation in Fig. 125, prolong the base 
line indefinitely and lay off upon it the distances ab, be, cd, 
etc., Fig. 126, each equal in length to a side of the hex. At 
these points erect pers., and through the points i'2''^'^' draw 
hor. lines intersecting the pers. in 4, 3, 2, i, etc. At be 
draw the hex. a''b^'b'\e''e^\d'' of the last prob. for the base, and 
at I, 2 draw the section i, 2, 3, 4, 5, 6 for the top. 

Prob. 14, Fig. 127. — To draw the projs. of a right cylin- 
der 3" diam. and 3'' long, (i) When its axis is per. to the 
H.P. (2) Draw the true form of a section of the cylinder, 
when cut by a plane per. to the V.P. making an angle of 30° 
with the H.P. (3) Draw a development of the upper part of 
the cyl. 

For the plan of the first condition, describe the circle i\ 
2' , etc., with a radius = i\" and from it project the eleva- 
tion, which will be a square of 3'^ sides. 

For the second condition: Let i, 7 be the trace of the 
cutting plane, making the point 7, ^' from the top of the cyl. 
Divide the circle into 12 equal parts and let fall pers. through 
these divisions to the line of section, cutting it in the points 
I, 2, 3,4, etc. Parallel to the line of section I, 7 draw Vj'^ 
at a convenient distance from it, and through the points 
I, 2, 3, 4, etc., draw pers. to 1,7, intersecting and extending 
beyond i" f . Lay off on these pers. the distances 6"%" = 
6'8', and 5^9" = S'q', etc., and through the points 2", i'\ 
4", etc., describe the ellipse. 

For the development: In line with the top of the eleva- 
tion draw the line ^'^'' equal in length to the circumference of 
the circle, and divide it into 12 equal parts a\ b' , etc., a', b" , 
etc. Through these points drop pers. and through the points 



92 



MECHANICAL DRA WING. 



I, 2, 3, etc., draw hors. intersecting the pers. in the points 
I, 2, 3, etc., and through these points draw a curve. 

Tangent to any point on the straight line draw a 3'' circle 
for the top of the cyl. and tangent to any suitable point on 
the curve transfer a tracing of the ellipse. 

Prob. 15, Fig. 128. — Draw the projections of a right cone 
']" high, with a base 6" in diam., pierced by aright cyl. 2" in 



g' f e 




Fig. 127. 



diam. and ^" long their axes intersecting at right angles 3" 
above the base of the cone and par. to V.P. Draw first the 
plan of the cone with a radius = Zk" • 

At a convenient distance below the plan draw the elevation 
to the dimensions required. 

3'' above the base of the cone draw the center line of the 
cyl. CD, and about it construct the elevation of the cyl., which 
will appear as a rectangle 2" wide and 2^" each side of the 
axis of the cone. The half only appears in the figure. 



ORTHOGRAPHIC FROJECTIOX 



93 



To project the curves of intersection between the cyl. and 
cone in the plan and elevation: Draw to the right of the cyl. 
on the same center line a semicircle with a radius equal that 
of the cyl. Divide the semicircle into any number of parts, 




Fig. 128. 



Fig. 129. 



as I, 2, 3, 4, etc. Through i, i draw the per. A" \" equal 
in length to the height of the cone, and through A" draw the 
line y^ ''4" tangent to the semicircle at the point 4, and through 
the other divisions of the semicircle draw lines from A" to the 
line \" ^\ meeting it in the points '^"2" . 

From all points on the line i"4", viz., \"2"i"d^' , erect 



94 ME CHA NIC A L DRA WING. 

pers. to the center line of the plan, cutting it in the points 
i/'2/'3/'4,'', and with i/' as the center draw the arcs 2/^-2, 
3/'-3, 4/^-4 above the center line of the plan, and through the 
points 2, 3, 4 draw hors. to intersect the circle of the plan in 
the points 2'3'4', and lay off the same distances on the other 
side of the center line of the plan in same order, viz., 2'3'4'. 
Through each of these points on the circumference of the circle 
of the plan draw radii to its center A\ and through the same 
points also in the plan let fall pers. to the base of the elevation 
of the cone, cutting it in the points 2'3'4' ; and from the apex 
A of the elevation of the cone draw lines to the points 2^34' on 
the base. Hor. lines drawn through the points of division 2, 
3, 4 on the semicircle will intersect the elements A~2\ A-j\ 
A— 4 of the cone in the points 2'3'4'; these will be points in 
the elevation of the curve of intersection between the cylinder 
and the cone. 

The plan of the curve is found by erecting pers. through 
the points in the elevation of the curve to intersect the radial 
lines of the plan in correspondingly figured points, through 
which trace the curve as shown. Repeat for the other half 
of the curve. 

Prob. 16, Fig. 129. — To draw the development of the 
half cone, showing the hole penetrated by the cyl. 

With center 4/', Fig. 129, and element ^i' of the cone, 
Fig. 128, as radius, describe an arc equal in length to the semi- 
circle of the base of the cone. Bisect it in the line 4/^1, and 
on each side of the point i lay off the distances 2, 3, 4, equal 
to the divisions of the arc in the plan Fig. 128, and from these 
points draw lines to 4", the center of the arc. Then with 
radii A-a, d, c, d, e, respectively, on the elevation Fig. 128, 



OK THOGRA PHIC PR OJE CTION. 



95 



and center 4," draw arcs intersecting the lines drawn from the 
arc XX ^.o its center 4/'. Through the points of intersection 
draw the curve as shown by Fig. 129. 

Prob. 17, Fig. 130. — To draw the development of the 
half of a truncated cone, given the plan and elevation of 
the cone. 




Fig. 130. 

Divide the semicircle of the plan into any number of parts, 
then with A as center and A i as radius, draw an arc and lay 
off upon it from the point I the divisions of the semicircle 
from I to 9, draw 9^. Then with' center yi and radius y^^ 
draw the arc BC. iBCg is the development of the half of 
the cone approximately. 



96 



MECHAXICAL DRA WIXG. 



Prob. 1 8, Fig. 131. — To draw the cun^e of intersection of 
a small cyl. with a larger. To the left of the center-line of 
Fig. 131 is a half cross-section, and to the right a half eleva- 
tion of the two cyls. 

Draw the half plan of the small cyl., which will be a 
semicircle, and divide it into any convenient number of parts, 
say 12. 

From each of these div^isions drop pers. 

On the half cross-section these pers. intersect the circum- 
ference of the large cyl. in the points i', 2', etc. Through 



Fig. 134. 



Fig. 133. 




5 4- 3 t 1 .1 I i s i- 5 6 




Fig. 132. 



these points draw hors. to intersect in corresponding points 
the pers. on the half elevation. Through the latter points 
draw the curve of intersection C. 

Prob. 19. — To draw the development of the smaller cyl. 
of the last prob. 

Draw a rectangle, Fig. 132, with sides equal to the circum- 



ORTHOGRAPHIC PROJECTION. 97 

ference and length of the cyl. respectively, and divide it into 
24 equal parts. 

]\Iake AB, i i', 3 3', etc., Fig. 132, equal to AB, I'l" , 
- 2", 2)'z'\ etc., Fig. 131, and draw the developed curve of 
intersection. 

PrOB. 20. — To draw the orthographic projections of a 
cylindrical dome riveted to a cylindrical boiler of given 
dimensions. 

Let the dimensions of the dome and boiler be : dome 
26h" diam. X ^j" high, boiler 54'' diam., plates i-" thick. 

Appl}- to the solution of this problem the principles ex- 
plained in Prob. No. 18, Fig. 131. 

When your drawings are completed, compare them with 
Figs. 133 and 134, which are the projections required in the 
problem. 

Letter or number the drawing and be prepared to explain 
how the different projections were found. 

Prob. 21. — To draw the development of the top gusset- 
sheets of a locomotive wagon-top boiler of given dimensions. 

First draw the longitudinal cross-section of the boiler to 
the dimensions given by Fig. 135, using the scale of i'^ = 
I ft. 

Then at any convenient point on your paper draw a 
straight line, and upon it lay off a distance AB 35-2'' long = 
the straight part of the top of the gusset-sheet G, Fig. 135. 
With center A and a radius = 2"/^" (the largest radius of the 
gusset) 4" 6" (the distance from the center of the boiler to the 
center of the gusset C, Fig. 135) = 33I", draw arc i. 

With center i5 and a radius = 26f (the smallest radius of 
the gusset) draw arc 2. Tangent to these arcs draw the 



98 



MECHANICAL DKA WING. 



Straight line i, 2 extended, and through the points A and 
draw lines i, A and 2, B per. to i, 2. 




Take a point on the per. i, 2, 6" from the point i as a 
center and through the point A draw an arc with a radius 



= 27i . 



ORTHOGRAPHIC PROJECTION, 99 

vVith point 2 as a center and 2B as a radius {26^") draw 
an arc through B to meet the line 1,2. 

Divide both arcs into any number of parts, say 12, and 
through these divisions draw Hnes per. to and intersecting \A 
and 2B respectively. Through these intersections draw in- 
definite hors. and on these hors. step off the length of the 
arcs, with a distance = one of the 12 divisions as follows: 

On the first hors. lay off the length of the arc A\' and B\' 
= ^i and B\ respectively. Then from i' lay off the same 
distance to 2' on the second hors. etc. Through these points 
draw curves Ai^' and B\2' . Join points 12' and 13' with a 
straight line. Then AB12, 13 will be the developed half of 
the straight part of the gusset. 

On the two ends or front and back of the gusset we have 
now to add i'' for clearance + 3!" for lap -|- -J'^ allowance 
for truing up the plates, total = 5^''. And to the sides 2-|^' 
for lap -\- i" allowance for truing up, total = 3-g-''. 

The outline of the developed sheet may now be drawn to 
include these dimensions with as little waste as possible, as 
shown by Fig. 136. Extreme accuracy is necessary in mak- 
ing this drawing, as the final dimensions must be found by 
measurement. 

Prob. 22. — To draw the projections of a V-threaded 
screw and its nut of 3'' diam. and f pitch. 

Begin by drawing the center line C, Fig. 137, and lay off 
on each side of it the radius of the screw ii'\ Draw AB 
and 6B. Draw A6 the bottom of the screw, and on AB step 
off the pitch = ^" , beginning at the point A. 

On line 6D from the point 6 lay off a distance = half the 
pitch = f , because when the point of the thread has com- 



lOO 



MECHANICAL DRA WING. 



pleted half a revolution it will have risen perpendicularh^ a 
distance = half the pitch, viz., f". 

Then from the point 6" on 6Z> step off as many pitches as 
may be desired. From the points of the threads just found, 

B V 





Fig. 137. Fig. 13S. 

draw with the 30° triangle and T-square the V of the threads 
intersecting at the points b . . b . . the bottom of the threads. 

At the point O on line A6 draw two semicircles with radii 

II the top and bottom of the thread respectively. Divrde 

these into any number of equal parts and also the pitch Pinto 

the same number of equal parts. Through these divisions 

draw hors. and pers. intersecting each other in the points as 



ORTHOGRAPHIC PROJECTION. 



lOI 



shown by Fig. 137, which sliows an elevation partly in section 
and a section of a nut to fit the screw. Through the points 
of intersection draw the curves of the helices shown, using 
No. 3 of the " Sibley College Set" of Irregular Curves. 




Fig. 139. 

Prob. 22. — To draw the proj. of a square-threaded screw 
3'' diam. and \" pitch and also a section of its nut. 

The method of construction is the same as for the last 
problem, and is illustrated by Fig. 138. 

Prob. 22. — To draw the projections of a square double 
threaded screw of 3'' diam. and 2" pitch, and also a section of 
its nut. 



^' 



102 



MECHANICAL DRA WING. 



The solution of this problem is shown by Fig. 139, and 
further explanation should be unnecessary. 

Prob. 23. — To draw the curve of intersection that is 
formed by a plane cutting an irregular surface of revolution. 




Fig. 140. 
Figs. 140, 141, and 142 show examples of engine con- 
necting rod ends where the curve / is formed by the inter- 

>^ ^ 




B D 

Fig. 141. 

section of the flat stub end with the surface of revolution of 
the turned part of the rod. 



ORTHOGRAPHIC PROJECTION. 



103 



The method of finding the curves of intersection are so 
plainly shown by the figures that a detailed explanation • is 
deemed unnecessary. 




Fig. 142. 



SHADE LINES AND SHADING. 

Shade Lines are quite generally used on engineering work- 
ing drawings ; they give a relieving appearance to the projec- 
ting parts, improve the looks of the drawing and make it easier 
to read, and are quickly and easily applied. 

The SJiading of the curved surfaces of machine parts is 
sometimes practiced on specially finished drawings, but on 
working drawings most employers will not allow shading be- 
cause it takes too much time, and is not essential to a quick 
and correct reading of a drawing, especially if a system of 
shade lines is used. 

Some of the principles of shade lines and shading are 
given below, with a few problems illustrating their commonest 
applications. 

The shadows which opaque objects cast on the planes of 



1 04 ME CHA NI CA L DRA WING . 

projection or on other objects are seldom or never shown on 
a working drawing, and as the students in Sibley College are 
taught this subject in a course on Descriptive Geometry, it is 
omitted here. 

CONVENTIONS. 

The Source of Light is considered to be at an infinite dis- 
tance from the object, therefore the Rays of Light will be rep- 
resented by parallel lines. 

The Source of Light is considered to be fixed, and the Point 
of Sight situated in front of the object and at an infinite dis- 
tance from it, so that the Visual Rays are parallel to one 
another and per. to the plane of projection. 

Shade Lines divide illuminated surfaces from dark surfaces. 

Dark surfaces are not necessarily to be defined by those 
surfaces which are darkened by the shadow cast by another 
part of the object, but by reason of their location in relation 
to the rays of light. 

It is the general practice to shade-line the different pro- 
jections of an object as if each projection was in the same 
plane, e.g., suppose a cube. Fig. 143, situated in space in the 
third angle, the point of sight in front of it, and the direction 
of the rays of light coinciding with the diagonal of the cube, 
as shown by Fig. 144. Then the edges a'^b'^ b^'c" will be shade 
lines, because they are the edges which separate the illumin- 
ated faces (the faces upon which fall the rays of light) from 
the shaded faces, as shown by Fig. 144. 

Now the source of light being fixed, let the point of sight 
remain in the same position, and conceive the object to be re- 
volved through the angle of 90° about a hor. axis so that a 



OJ^ THOG RA PHIC PR OJE C TJ ON. 



105 



plan at the top of the object is shown above the elevation, and 
as the projected rays of light falling in the direction of the 
diagonal of a cube make angles of 45° with thehor. , then with 
the use of the 45° triangle we can easily determine that the 
lower and right-hand edges of the plan as well as of the ele- 
vation should be shade lines. 

This practice then will be followed in this work, viz. : 
Shade lines shall be applied to all projections of an object. 



a b 

Fig. 143. 



^-1 



'^^. 



A-- 

/ 



\ 



\ 



Fig. 144. 



considering the rays of light to fall upon each of them, from 
the same direction. 

Shade lines should have a width equal to 3 times that of 
the other outlines. Broken lines should never be shade lines. 

The outlines of surfaces of revolution should not be shade 
lines. The shade-lined figures which follow will assist in il- 
lustrating the above principles; they should be studied until 
understood. 



I06 MECHANICAL DRAWING. 



SHADING. 



The sJiade of an object is that part of the surface from 
which light is excluded by the object. 

The cine of sJiade is the line separating the shaded from 
the illuminated part of an object, and is found where the rays 
of light are tangent to the object. 

Brilliant Points. — " When a ray of light falls upon a sur- 
face which turns it from its course and gives it another direc- 
tion, the ray is said to be reflected. The ray as it falls upon 
the surface is called the incident ray, and after it leaves the 
surface the reflected ray. The point at which the reflection 
takes places is called the point of incidence. 

'' It is ascertained by experiment — 

'^ (ci) That the plane of the incident and reflected rays is 
always normal to the surface at the point of incidence ; 

" {U) That at the point of incidence the incident and re- 
flected rays make equal angles with the tangent plane or normal 
line to the surface. 

" If therefore we suppose a single luminous point and the 
light emanating from it to fall upon any surface and to be re- 
flected to the eye, the point at which the reflection takes place 
is called the brilliant point. The brilliant point of a surface 
is, then, the point at which a ray of light and a line drawn to 
the eye make equal angles with the tangent plane or normal 
line — the plane of the two lines being normal to the surface." 
— Davies : Shades and SJiadows. 

Considering the rays of light to be parallel and the point 
of sight at an infinite distance, the brilliant point on the sur- 
face of a sphere is found as follows: Let A^O and A^'0\ Fig. 



ORl 'HO G RA PHIC PR OJE C TION. 



107 



145, be a ray of light and A'"A^' a visual ray. Bisect the angles 
contained between the ray of light and the visual ray as fol- 
lows : Revolve A'O about the axis A" until it becomes parallel 
to the hor. plane at A'"C^ . At C^ erect a per. to intersect 
a hor. through C^ at 6^/' join Cl'Ll' {L may be any convenient 




Fig. 145. 



point on the line of vision), bisect the angle ZM'^^'^'^ with the 
line A^'iy\ Join C'V and through the point D^\ draw a hor. 
cutting C^D- at Dl\ then A^'D^' is the hor. projection of the 
bisecting line. A plane drawn per. to this bisecting line and 
tangent to 'the sphere touches the surface at the points 
R'^Bl'' where the bisecting lines pierce it. Therefore B"B'' are 
the two projections of the brilliant point. 



io8 



ME CHA NICA L DRA WING. 



TJie point of shade can be found as follows: 
Draw A^'G, Fig, 145, making an angle of 45° with a hor. 
Join the points E and i^ with a straight line EF. Lay off on 
A''G a distance equal to EF, and join EG. Parallel to EG 
Fig. 146. Fig. 147. 





Fig. 148. 
draw a tangent to the sphere at the point T. Through T 
draw TP' per. to A^'G. From the point P^ drop a per. to P\ 
P" is the point of shade. 

Prob. 24. — To shade the elevation of a sphere with graded 
arcs of circles. 



OR THOGRA PHIC PROJECTION 



109 



First find the brilliant point and the point of shade, and 
divide the radius I, 2 into a suitable number of equal parts, 
and draw arcs of circles as shown by Fig. 146, grading them 
by moving the center a short distance on each side of the 
center of the sphere on the line B^-2 and varying the length of 
the radii to obtain a grade of line that will give a proper 
shade to the sphere. It is desirable to use a horn center to 
protect the center of the figure. 

Pig. 149 shows the stippling method of shading the 
sphere. 






Fig. 149. 



Fig. 150. 



PrOB. 25,— To shade a right cylinder with graded right 
lines. 

Find the line of light B'"' by the same method used to find 
the brilliant point on the sphere, except that the line of light 
is projected from the point B^' where the bisection line A^D 
cuts the circle of the cylinder. 

The line of shade is found where a plane of rays is tan- 
gent to the cyl. at S' and S'-. 

Fig. 150 shows how the shading lines are graded from 
the line of shade to the line of light. 

It will be noticed that the lines grow a little narrower to 
the right of the line of shade on Fig. 150; this shows where 



no 



MECHANICAL DRAWING, 



the reflection of the rays of light partly illumine the outline 
of the cylinder. 

Prob. 26, Fig. 148. — To shade a right cone with graded 
right lines tapering toward the apex of the cone. 

Find the elements of light and shade as shown by Fig. 148, 
and draw the shading-lines as shown by Fig. 151, grading 
their width toward the light and tapering them toward the 
apex of the cone. 





Fig. 151. 



Fig. 152. 



The mixed appearance of the lines near the apex of the 
cone on Fig. 151 can usually be avoided by letting each line 
dry before drawing another through it, or as some draftsmen 
do, stop the lines just before they touch. 

Prob. 27. — To shade the concave surface of a section of a 
hollow cylinder. 

Find the element of light and grade the shading lines from 
it to both edges as shown by Fig. 152. 

Fig. 153 shows a conventional method of shading a hex- 
agonal nut. 

Prob. 28. — To draw a front and end elevation of a rect- 
angular hollow box with a rectangular block on each face, each 



OR THO GRA PHJC PR OJE C TION. 



Ill 



block to have a rectangular opening, and all to be properly 
shade-lined and drawn to the dimensions given on Fig. 154. 




Fig. 153- 
Draw the hor. center line first, and then the vertical center 
line of the end view. About these center lines on the end el- 

FiG. 154. 




Fig. 155. 
evation construct the squares shown and erect the edges of the 
blocks. Next draw the hidden lines indicating the thickness 



I 1 2 MECHA NIC A L DRA WING. 

of the walls of the box and the openings through the blocks, 
measuring the sizes carefully to the given dimensions. 

Draw the front elevation by projecting lines from the va- 
rious points on the end elevation, and assuming the position of 
the line AB measure off the lengths of the hor. lines and erect 
their vert, boundaries as shown by the figure. 

Prob. 29. — Given the end elevation of the last prob., cut 
by three planes A^ B and C, Fig. 155. Draw the projections 
of these sections when the part to the left of the cutting plane 
has been removed, and what remains is viewed in the direction 
of the arrow, remembering that all the visual rays are parallel. 

These drawings and all that may follow are to be properly 
shade-lined in accordance with the principles given above. 

ISOMETRICAL DRAWING. 

In orthographic projection it is necessary to a correct 
understanding of an object to have at least two views, a front 
and end elevation, or an elevation and plan, and sometimes 
even three views are required. 

Isometric drawing on the other hand shows an object com- 
pletely with only one view. It is a very convenient system 
for the workshop. Davidson in his Projection calls it the 
" Perspective of the Workshop." It is more useful than per- 
spective for a working drawing, because, as its name implies 
(" equal measures ") it can be made to any scale and measured 
like an orthographic drawing. It is, however, mainly em- 
ployed to represent small objects, or large objects drawn to a 
small scale, whose main lines are at right angles to each other. 

The principles of isometrical drawing are founded on a 
cube resting on its lower front corner, i. Fig. 156, and its base 



OK THO G RA PHIC PR OJE C TION. 



113 



elevated so that its diagonal AB is parallel to the horizontal 
plane. Then if the cube is rotated on the corner i until the 
diagonal AB is at right angles to the vert, plane, i.e., 
through an angle of 90°, the front elevation will appear as 
shown at i, 2, 3, 4, Fig. 156, a regular hexagon. 

Now we know that in a regular hexagon, as shown by Fig. 
156, the lines \A, ^3, etc., are all equal, and are easily drawn 




Fig. 156. 



with the 30° X 60° triangle. But although these lines and 
faces appear to be equal, yet, being inclined to the plane of 
projection, they are shorter than they would actually be on 
the cube itself. However, since they all bear the same pro- 
portion to the original sizes, they can all be measured with 
the same scale. 

We will now describe the method of making an isomet- 
rical scale. 

Draw the half of a square with sides = 2^" , Fig. 157. 
These two sides will make the angle of 45° with the horizontal. 
Now the sides of the corresponding isometrical square, we have 
seen, make the angle of 30° with the horizontal, so we will 



114 



ME CHANICAL D RA WING. 



draw 14, 3 4, making angles of 30° with i, 3. The differ- 
ence then between the angle 2, i, 3 and the angle 4, i, 3 is 
15°, and the proportion of the isometrical projection to the 
actual object is as the length of the line 3, 2 to the line 3, 4. 
And if the line 3, 2 be divided into any number of equal parts, 
and lines be drawn through these divisions par. to 2, 4 to cut 
the line 3, 4 in corresponding divisions, these will divide 3, 4 
proportionately to 3, 2. 

Now if the divisions on 3, 2 be taken to represent feet 
and those on 3, 4 to represent 2 feet, then 3, 4 would be an 
isometrical scale of \. 




Fig. 157. 



Since isometrical drawings may be made to any scale, we 
may make the isometrical lines of the object = their true size. 
This is a common practice and precludes the need of a special 
isometrical scale. 

The Direction of the Rays of Light. — The projection of a 
ray of light in isometrical drawing will make the angle of 30° 
with the horizontal as shown by the line 3, 2 on the front 
elevation of the hex.. Fig. 156. And the sJiade lines will be 
applied as in ordinary projection. 

Prob. 30. — To make the isometrical drawing of a two- 
armed cross standing on a square pedestal. 



OR THO GRA PHIC PR OJE C TIOiV. 



115 



Begin by drawing a center line AB, Fig. 158, and from the 
point A draw AC and AD, making an angle of 30° with the 
horizontal. Measure from A on the center line AB a dis- 
tance - -{\" , and draw lines par. to AC, AB; make AC and 
AD 2^'^ long and erect a perpendicular at D and C, complet- 
ing the two front sides of the base, etc. 




Fig. 158. 



Prob. 31. — To make the isometrical drawing of a hollow 
cube, with square block on each face and a square hole 
through each block, to dimensions given on Fig. 159. 

As before, first draw a center line, and make an isometrical 
drawing of a 2^'' cube, and upon each face of it build the 
blocks with the square holes in them, exactly as shown in 
Fig. 159. 

Prob. 32. — To project an isometrical circle. 

The circle is enclosed in a square, as shown by Fig. 160. 



Ii6 



ME CHA Nl CA L DRA WING. 



Draw the circle with a radius =-2" and describe the square 
I, 2, 3, 4 about it. 

Draw the diagonals i, 2, 3, 4 and the diameters 5, 6, 7, 8 



at right angles to each other. 



Now from the points i and 2 draw lines \A, \B and 2 A, 
2B, making angles of 30° with the hor. diagonal 1,2. And 




Fig. 159 

through the center O draw CD and EF at right angles to the 
isometrical square. 

The points CD, EF, and GH will be points in the curve 
of the projected isometrical circle, which will be an ellipse. 
The ellipse may be drawn sufficiently accurate as follows : 
With center B and radius BC describe the arc CF 3.nd ex- 
tend it a little beyond the points C and F, and with center A 
and same rad. describe a similar arc, then with a rad. which 



OR THO GRA PHI C PR OJECTION. 



117 




Fig. 160. 



Fig. 161. 




Fig. 164. 



Fig. 165. 



Il8 MECHANICAL DRAWING. 

may readily be found by trial, draw arcs through the points 
G and H and tangent to the two arcs already described. 

Figs. i6i, 162, 163, 164, 165, and 166 are for practice in 
the application of the preceding principles, and at least one 
of these should be drawn, or it would be better still if the stu- 




FlG. 166. 

dent would attempt to make an isometrical projection of his 
instrument-box, desk, or any familiar object at hand. These 
figures may be measured with the \\" scale and drawn with 
the 2" scale. 

WORKING DRAWINGS. 

Working drawings are sometimes made on brown detail- 
paper in pencil, traced on tracing-paper or cloth, and then 
blue printed. 

The latter process is accomplished as follows : 

The tracing is placed face down on the glass in the print- 
ing-frame, and the prepared paper is placed behind it, with 
the sensitized surface in contact with the back of the tracing. 

In printing from a negative the sensitized surface of the 
prepared paper is placed in contact with the film side of the 
negative, and the face is exposed to the light. 

The blue-print system for working drawings has many 
drawbacks, e.g., the sectioned parts of the drawing require to 



ORTHOGRAPHIC PROJECTION. II9 

be hatch-lined, using the standard conventions already re 
ferred to for the different materials. This takes a great deal 
of time. The print has usually to be mounted on cardboard, 
although this is not always done, and unless it is varnished 
the frequent handling with dirty, oily fingers soon makes it 
unfit for use. 

Changes can be made on the prints with soda-water, it is 
true, but they seldom look well, and when many changes or 
additions require to be made it is best to make them on the 
tracing and take a new print. And the sunlight is not always 
favorable to quick printing. So taking everything into con- 
sideration the system of making working drawings directly on 
cards and varnishing them is probably the best. It is the 
system used by the Schenectady Locomotive Works and 
many other large engineering establishments. In size the 
cards are made 9" X 12", 12" X 18'', 18" X 24''; they are 
made of thick pasteboard mounted with Irish linen record- 
paper. The drawings are pencilled and inked on these cards 
in the usual way, and the sections are tinted with the conven- 
tional colors, which are much quicker applied than hatch- 
lines. The face of the drawing is protected with two coats of 
white shellac varnish, while the back of the card is usually 
given a coat of orange shellac. 

The white varnish can easily be removed with a little 
alcohol, and changes made on the drawing, and when revar- 
nished it is again ready for the shop. 

We wall now^ try to describe what a working drawing is 
and what it is for. In the hands of an experienced workman 
a working drawing is intended to convey to him all the neces- 
sary information as to shape, size, material, and finish to 



I20 



MECHANICAL DRA WING. 




ORTHOGRAPHIC PROJECTION 



121 



Z^,.. 




122 MECHANICAL DRAWING. 

enable him to properly construct it without any additional in- 
structions. This means that it must have a sufficient num- 
ber of elevations, sections, and plans to thoroughly explain 
and describe the object in every particular. And these views 
should be completely and conveniently dimensioned. The 
dimensions on the drawing must of course give the sizes to 
which the object is to be made, without reference to the scale 
to which it may be drawn. The title of a working drawing 
should be as brief as possible, and not very large — a neat, 
plain, free-hand printed letter is best for this purpose. 

Finished parts are usually indicated by the letter " f," and 
if it is all to be finished, then below the title it is customary 
to write or print " finished all over." 

The number of the drawing may be placed at the upper 
left-hand corner, and the initials of the draftsman immedi- 
ately below it. 

A second-year course, entitled Mechanical Drawing and 
Elementary Machine Design, is in preparation, and will shortly 
be published. 

Figs. 167 and 168 show working drawings of two shaft- 
couplings, fully figured, sectioned, and shade-lined. 



INDEX. 



A 

PAGE 

Angle, To bisect an 19 

Angle, To construct an 15 

Anti-friction curve, " Schiele's " 50 

Arched window-opening, To draw an 53 

Arkansas oil-stones 5 



B 

Baluster, To draw a 53 

Board, Drawing i 

Bow instruments 2 

Brass, Sheet of 6 

Breaks, Conventional 61 

Brilliant points 106 



C 

Celluloid, Sheet of thin 5 

Center lines 60 

Cinquefoil ornament. To draw the 53 

Circle, Arc of a, To find the center of an , 32 

Circle, Arc of a. To draw a line tangent to an 33 

Circle, To draw a right line equal to half the circumference of a 31 

Circle, To draw a tangent between two 33 

Circle, To draw tangents to two 34 

Circle, To draw an arc of a, tangent to two straight lines 34 

Circle, To inscribe a, within a triangle 35 

Circle, To draw an arc of a, tangent to two circles 36 

Circle, To draw an arc of a, tangent to a straight line and a circle 37 

Circle, To construct the involute of a 45 

Circle, To find the length of an arc of a, approximately 47 

123 



124 INDEX. 

PACK 

Cissoid, To draw the 4g 

Compass 2 

Conventions 56 

Conventions, Shading 104 

Conventional breaks 61 

Conventional lines 60 

Conventional screw-threads 62 

Cross-sections 62 

Curves, Irregular 3 

Cycloid, To describe the 46 



D 

Dark surfaces 104 

Development of the surfaces of a hexagonal prism go 

Development of the surface of a right cylinder 92 

Development of the surface of a cone 93 

Development of the surface of a cylindrical dome 96 

Development of a locomotive gusset sheet 97 

Dihedral angles 75 

Direction, The, of the rays of light 105 

Dividers, Hair-spring 2 

Drawing-board i 

Drawing-pen ... 2 

Drawing to scale 12, 54 



E 

Ellipse, To describe an - , 38 

Ellipse, Given an, to find the axes and foci 43 

Epicycloid, To describe the 48 

Epicycloid, To describe an interior , . . . . 50 

Equilateral triangle, To construct an 24 

Examples of working drawings 120 

F 

Figuring and lettering 66 

Finished parts of working drawings. 122 

G 

Geometrical drawing , 16 

Glass-paper pencil sharpener 4 

Gothic letters > 69 



INDEX. 125 

H 

PAGE 

Heptagon, To construct a 28 

Hyperbola, To draw an 42 

Hypocycloid, To describe the 48 



I 

Ink eraser 4 

Inks 4 

Instruments 2 

Intersection, The, of a cylinder with a cone 93 

Intersection, The, of two cylinders g6 

Intersection, The, of a plane with an irregular surface of revolution 102 

Involute, of a circle, To construct the , 45 

Isometrical cube 113 

Isometrical drawing 112 

Isometrical drawing, Direction of the rays of light in. . . 114 

Isometrical drawing of a two-armed cross 115 

Isometrical drawing of a hollow cube 116 

Isometrical drawing, Examples of 117 

Isometrical scale, The 114 



L 

Leads for compass 13 

Lettering and figuring. 64 

Line of shade 106 

Line, To draw a, parallel to another ig 

Line, To divide a 21 

Line of motion 60 

Line of section 60 



M 

Mechanical drawing and elementary machine design 122 

Model of the co-ordinate planes 81 

Moulding, The "Scotia " 51 

Moulding, The " Cyma Recta" 51 

Moulding, The "Cavetto " or " Hollow " 51 

Moulding, The " Echinus, " " Quatrefoil," or " Ovolo " 52 

Moulding, The " Apophygee " 52 

Moulding, The " Cyma Reversa " 52 

Moulding, The "Torus" 52 



126 INDEX. 



N 

PAGE 

Needles 6 

Notation 80 



O 

Octagon, To construct an 28 

Orthographic projection, . , . 74 

Oval, To construct an 43 



P 

Paper , 2 

Parabola, To construct a /. 41 

Pencil 2 

Pencil eraser 4 

Pencil, To sharpen the 8 

Pen, Drawing 9 

Pen, To sharpen the drawing 10 

Pentagon, To construct a 28 

Perpendicular, To erect a 17 

Planes of projection. The 75 

Polygon, To construct a 26 

Projection, The, of straight lines 82 

Projection, The, of plane surfaces 84 

Projection, The, of solids • go 

Projection, The, of the cone 93 

Projection of the helix as applied to screw-threads 99 

Proportional, To find a mean, to two given lines 31 

Proportional, To find a thirds to two given lines 31 

Proportional, To find a fourth, to three given lines 32 

Protractor , 6 



Q 

Quatrefoil, To draw the 53 



R 

Rays of light 104 

Rays, Visual 104 

Rhomboid, To construct the 21 

Right angle. To trisect a 24 

Roman letters 67 



INDEX. 127 



S 

PAGE 

Scale guard 6 

Scale, Drawing to 12, 54 

Scale, To construct a 55 

Schiele's curve, To draw 50 

Screw-threads, Conventional 62 

Screw-threads, Regular 100 

Section lines , 56 

Section lines, Standard 58 

Shade lines and shading 103 

Shade, To, the elevation of a sphere 108 

Shade, To, a right cylinder 109 

Shade, To, a right cone no 

Shade, To, a concave cylindrical surface no 

Sharpen pencil, To 8 

Sharpen pen. To 10 

Sheet brass ... 6 

Sheet celluloid 6 

*' Sibley College " set of irregular curves 3 

*' Sibley College " set of instruments 2 

Source of light 104 

Spiral, To describe the 44 

Sponge rubber 5 

Square, To construct a 25 

Stippling , 109 

T 

Tacks 5 

T-square 2 

Third dihedral angle 75 

Tinting brush 5 

Tinting saucer 5 

Title, The, of a working drawing 122 

Tracing-ck)th. . . 6 

Trefoil, To describe the 53 

Triangles 3 

Triangle, To construct a 25 

Triangular scale 3 

Type specimens 70 

U 

Use of instruments 7 

Use of pencil , 8 



128 INDEX. 



PAGE 



Use of drawing-pen , g 

Use of triangles n 

Use of T-square 1 1 

Use of drawing-board u 

Use of scale 12 

Use of compasses 13 

Use of dividers or spacers 13 

Use of spring bows 14 

Use of irregular curves 14 

Use of protractor 14 



V 

Visual rays 104 

Volute, To describe the " Ionic" 45 



W 

Water-colors 5 

Water glass 5 

Writing-pen 6 

Working drawings 118 

Working drawings, Method of making 119 

Working drawing, What is a 119 

Working drawings, Examples of 119 



SHORT-TITLE CATALOGUE 

OF THE 

PUBLICATIONS 

OF 

JOHN WILEY & SONS, 

New York. 

London: CHAPMAX & HALL, Limited. 

ARRANGED UNDER SUBJECTS. 



Descriptive circulars sent on application. 

Books marked with an asterisk are sold at net prices only. 

All books are bound in cloth unless otherwise stated. 



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Cattle Feeding— Dairy Practice — Diseases of Animals — 
Gardening, Etc. 

Armsby's Manual of Cattle Feeding 12mo, |1 75 

Downing's Fruit and Fruit Trees 8vo, 5 00 

Grotenfelt's The Principles of Modern Dairy Practice. (Woll.) 

12mo, 2 00 

Kemp's Landscape Gardening 12mo, 2 50 

Lloyd's Science of Agriculture 8vo, 4 00 

Loudon's Gardening for Ladies. (Downing.) 12mo, 1 50 

Steel's Treatise on the Diseases of the Dog 8vo, 3 50 

" Treatise on the Diseases of the Ox Svo, 6 00 

Stockbridge's Rocks and Soils Svo, 2 50 

Woil's Handbook for Farmers and Dairymen 12mo, 1 50 

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Berg's Buildings and Structures of American Railroads 4to, 7 50 

Birkmire's American Theatres — Planning and Construction. Svo, 3 00 

" Architectural Iron and Steel Svo, 3 50 

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" Planning and Construction of High Office Buildings. 

Svo, 3 50 
1 



Carpenter's Heating and Ventilating of Buildings 8vo, $3 00 

Downing, Cottages 8vo, 2 50 

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Freitag's Architectural Engineering Svo, 2 50 

Gerhard's Sanitary House Inspection 16mo, 1 00 

" Theatre Fires and Panics 12nio, 1 50 

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Holly's Carpenter and Joiner , . ISmo, 75 

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Merrill's Stones for Building and Decoration Svo, 5 00 

Mouckton's Stair Building — Wood, Iron, and Stone 4to, 4 00 

Wait's Engineering and Architectural Jurisprudence Svo, 6 00 

Sheep, 6 50 
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World's Columbian Exposition of 1893. 4to, 2 50 

ARMY, NAVY, Etc. 

MiLiTAEY ExGixEERiNG— Ordnance — Port Charges — Law, Etc. 

Bourne's Screw Propellers 4to, 

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Cronkhite's Gunnery for Non-com. Officers ISmo, morocco, 

Davis's Treatise on Military Law Svo. 

Sheep, 
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Dietz's Soldier's First Aid 12mo, morocco, 

* Dredge's Modern French Artillery 4to, half morocco, 

Record of the Transportation Exhibits Building, 
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Durand's Resistance and Propulsion of Ships .8vo, 

Dyer's Light Artillery 12mo, 

Hoff's Naval Tactics Svo, 

Hunter's Port Charges Svo, half morocco, 

Ingalls's Ballistic Tables Svo, 

2 



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6 00 


4 00 


3 00 


12 50 


2 00 


7 00 


7 50 


2 00 


1 25 


20 00 


10 00 


5 00 


3 00 


1 50 


13 00 


1 50 



Ingalls's Haudbook of Problems in Direct Fire 8vo, 4 00 

Mahau's Advanced Guard 18mo, $1 50 

Mabau's Permanent Fortifications. (Mercur.).8vo, balf morocco, 7 50 

Merciir's Attack of Fortified Places 12mo, 2 00 

Mercur's Elements of the Art of War 8vo, 4 00 

Metcalfe's Ordnance and Gunnery 12mo, with Atlas, 5 00 

Murray's A Manual for Courts-Martial 18mo, morocco, 1 50 

" Infantry Drill Regulations adapted to tbe Springfield 

liifle, Caliber .45 18mo, paper, 15 

Pbelps's Practical Marine Surveying 8vo, 2 50 

Powell's Army Officer's Examiner 12m o, 4 00 

Reed's Signal Service , 50 

Sbarpe's Subsisting Armies 18mo, morocco, 1 50 

Very's Navies of tbe World 8vo, balf morocco, 8 50 

Wbeeler's Siege Operations , 8vo, 2 00 

Wintbrop's Abridgment of Military Law 12mo, 2 50 

WoodbuU's Notes on Military Hygiene 12mo, morocco, 2 50 

Young's Simple Elements of Navigation.. l2mo, morocco flaps, 2 50 

first edition 1 00 

ASSAYIiNQ. 

Smelting — Ore Dressing— Alloys, Etc. 

Fletcber's Quant. Assaying witb tbe Blowpipe.. 12mo, morocco, 1 50 

Furman's Practical Assaying 8vo, 3 00 

Kuubardt's Ore Dressing 8vo, 1 50 

* Mitchell's Practical Assaying. (Crookes.) 8vo, 10 00 

O'Driscoll's Treatment of Gold Ores 8vo, 2 00 

Ricketts and Miller's Notes on Assaying 8vo, 3 00 

Thurston's Alloys, Brasses, and Bronzes 8vo, 2 50 

Wilson's Cyanide Processes 12mo, 1 50 

" Tbe Cblorination Process 12mo, 150 

ASTRONOMY. 

Practical, Theoretical, and Descriptive. 

Craig's Azimuth 4to, 3 50 

Doolittle's Practical Astronomy 8vo, 4 00 

Gore's Elements of Geodesy 8vo, 2 50 

Michie and Harlow's Practical Astronomy 8vo, 3 00 

White's Theoretical and Descriptive Astronomy 12mo, 2 00 

3 



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Gardening for Ladies, Etc. 

Baldwin's Orchids of New England 8vo, $1 50 

Loudon's Gardening for Ladies. (Downing.) 12mo, 1 50 

Thome's Structural Botany 18mo, 2 25 

Westermaier's General Botany. (Schneider. ) 8vo, 2 00 

BRIDGES, ROOFS, Etc. 

Cantilever — Draw — Highway — Suspension. 
{See also Engineering, p. 6.) 

Boiler's Highway Bridges Svo, 

* " The Thames River Bridge 4to, paper, 

Burr's Stresses in Bridges. Svo, 

Crehore's Mechanics of the Girder Svo, 

Dredge's Thames Bridges 7 parts, per part, 

Du Bois's Stresses in Framed Structures 4to, 

Foster's Wooden Trestle Bridges 4to, 

Greene's Arches in Wood, etc Svo, 

Bridge Trusses Svo, 

" Roof Trusses Svo, 

Howe's Treatise on Arches Svo, 

Johnson's Modern Framed Structures .■ . . . .4to, 

Merriman & Jacoby's Text-book of Roofs and Bridges. 

Part I. , Stresses Svo, 

Merriman & Jacoby's Text-book of Roofs and Bridges. 

Part IL, Graphic Statics, Svo, 

Merriman & Jacoby's Text-book of Roofs and Bridges. 

Part III., Bridge Design Svo, 

Merriman & Jacoby's Text-book of Roofs and Bridges. 

Part IV., Continuous, Draw, Cantilever, Suspension, and 

Arched Bridges Svo, 

*Morison's The Memphis Bridge Oblong 4to, 

Waddell's Iron Highway Bridges Svo, 

" De Pontibus (a Pocket-book for Bridge Engineers). 

Wood's Construction of Bridges and Roofs Svo, 

Wright's Designing of Draw Spans Svo, 

4 



2 00 


5 00 


3 50 


5 00 


1 25 


10 00 


5 00 


2 50 


2 50 


1 25 


4 00 


10 00 


2 50 


2 50 


2 50 



2 50 


.0 00 


4 00 


2 00 


2 50 



CHEMISTRY. 

Qualitative — Quantitative — Organic — Inorganic, Etc. 

Adriance's Laboratory Calculations 12mo, 

Allen's Tables for Iron Analysis 8vo, 

Austen's Notes for Chemical Students 12mo, 

Bolton's Student's Guide in Quantitative Analysis 8vo, 

Classen's Analysis by Electrolysis. (Herrick and Boltwood.).8vo, 

Craf ts's Qualitative Analysis. (Schaeffer. ) 12mo, 

Drecbsel's Chemical Reactions. (Merrill.) 12mo, 

Fresenius's Quantitative Chemical Analysis. (Allen.) Svo, 

Qualitative " " (Johnson.) Svo, 

(Wells) Trans. 16th. 

German Edition Svo, 

Fuerte's Water and Public Health , , 13mo, 

Gill's Gas and Fuel Analysis 12mo, 

Hammarsten's Physiological Chemistry. (Mandel.) Svo, 

Helm's Principles of Mathematical Chemistry. (Morgan). 12mo, 

Kolbe's Inorganic Chemistry 12mo, 

Ladd's Quantitative Chemical Analysis 12mo. 

Landauer's Spectrum Analysis. (Tingle.) Svo, 

Mandel's Bio-chemical Laboratory, , 12mo, 

Mason's Water-supply Svo, 

" Analysis of Potable Water. {In the press.) 

Miller's Chemical Physics Svo, 

]\Iixter's Elementary Text-book of Chemistry 12mo, 

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O'Brine's Laboratory Guide to Chemical Analysis Svo, 

Perkins's Qualitative Analysis 12mo, 

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Poole's Calorific Power of Fuels Svo, 

Ricketts and Russell's Notes on Inorganic Chemistry (Non- 
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Ruddiman's Incompatibilities in Prescriptions Svo, 

Schimpf's Volumetric Analysis 12mo, 

Spencer's Sugar Manufacturer's Handbook . 12mo, morocco flaps, 
*' Handbook for Chemists of Beet Sugar House. 

12mo, morocco, 3 00 
5 



11 35 


3 00 


1 50 


1 50 


3 00 


1 50 


1 25 


6 00 


3 00 


5 00 


1 50 


1 25 


4 00 


1 50 


1 50 


3 00 


1 50 


5 00 


2 00 


1 50 


1 00 


2 50 


2 00 


1 00 


1 50 


3 00 


75 


2 00 


2 50 


2 00 



Stockbridge's Rocks aud Soils 8vo, $2 50 

Troilius's Chemistiy of Irou 8vo, 2 00 

Wells's Qualitative Analysis 12mo. 

Wiecbmauu's Chemical Lecture Notes 12rao, 3 00 

" Sugar Analysis 8vo, 2 50 

Wulling's Inorganic Pbar. and Med. Cbemistry 12mo, 2 00 

DRAWING. 

Elementaky — Geometrical — Topographical. 

Hill's Shades and Shadows and Perspective Svo, 2 00 

MacCord's Descriptive Geometry Svo, 3 00 

MacCord's Kinematics ,. Svo, 5 00 

" Mechanical Drawing Svo, 4 00 

Maban's Industrial Drawing. (Thompson.) 2 vols., Svo, 3 50 

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Reid's A Course in Mechanical Drawing . . .'. Svo. 2 00 

" Mechanical Drawing and Elementary Mechanical Design. 

Svo. 

Smith's Topographical Drawing. (Macmillan.) Svo, 2 50 

Warren's Descriptive Geometry 2 vols., Svo, 3 50 

" Drafting Instruments 12mo, 1 25 

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" Higher Linear Perspective Svo, 3 50 

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" Machine Construction 2 vols., Svo, 7 50 

Plane Problems , 12mo, 125 

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Shades and Shadows Svo, 3 00 

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Anthony and Brackett's Text-book of Physics (Magie). . . Svo, 4 00 

Barker's Deep-sea Soundings Svo, 2 00 

Benjamin's Voltaic Cell Svo, 3 00 

•' History of Electricity Svo 3 00 

6 



3 00 


35 00 


7 50 


2 50 


2 00 


4 00 


1 00 


2 50 


2 00 


1 50 


1 50 



Cosmic Law of Thermal Repulsiou ISmo, $ 75 

Crehore aud Squiei's Experimeuts with a New Polarizing- Photo- 
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* Dredge's Electric Illumiuations. . . .2 vols., 4to, half morocco, 

Vol.11 4to, 

Gilbert's De maguete. (Mottelay.) 8vo, 

Holmau's Precision of Measurements 8vo, 

Michie's Wave Motion Relating to Sound and Light, 8vo, 

Morgan's The Theory of Solutions and its Results 12mo, 

Niaudet's Electric Batteries. (Fishback.) .12mo, 

Reagan's Steam and Electrical Locomotives 12mo, 

Thurston's Stationary Steam Engines for Electric Lighting Pur- 
poses 12mo, 

Tillman's Heat 8vo, 

ENGINEERING. 
Civil — Mechanical— Sanitary, Etc. 

^ee also Bridges, p. 4 ; Hydraulics, p. 8 ; Materials op En- 
gineering, p. 9 ; Mechanics and Machinery, p. 11 ; Steam Engines 
AND Boilers, p. 14.) 

Baker's Masonry Construction 8vo, 5 00 

Baker's Surveying Instruments 12mo, 3 00 

Black's U. S. Public Works 4to, 5 00 

Brook's Street Railway Location 12mo, morocco, 1 50 

Butts's Engineer's Field-book 12mo, morocco, 2 50 

Byrne's Highway Construction 8vo, 7 50 

Carpenter's Experimental Engineering 8vo, 6 00 

Church's Mechanics of Engineering — Solids and Fluids 8vo, 6 00 

" Notes and Examples in Mechanics 8vo, 2 00 

Crandall's Earthwork Tables : 8vo, 1 50 

Crandall's The Transition Curve 12mo, morocco, 1 50 

* Dredge's Penn. Railroad Construction, etc. . . Folio, half mor., 20 00 

* Drinker's Tunnelling 4to, half morocco, 25 00 

Eissler's Explosives — Nitroglycerine and Dynamite 8vo, 4 00 

Gerhard's Sanitary House Inspection 16mo, 1 00 

Godwin's Railroad Engineer's Field-book. 12mo, pocket-bk.form, 2 50 

Gore's Elements of Geodesy , 8vo, 2 50 

Howard's Transition Curve Field-book 12mo, morocco flap, 1 50 

Howe's Retaining Walls (New Edition.) 12mo, 1 25 

7 



Hudson's Excavation Tables. Vol. II 8vo, |1 00 

Hutton's Mechanical Engineering of Power Plants 8vo, 5 00 

Johnson's Materials of Construction 8vo, 6 00 

Johnson's Stadia Reduction Diagram. .Sheet, 22^ X 28^ inches, 50 

" Theory and Practice of Surveying 8vo, 4 00 

Kent's Mechanical Engineer's Pocket-book 12mo, morocco, 5 00 

Kiersted's Sewage Disposal 12mo, 1 25 

Kirkwood's Lead Pipe for Service Pipe 8vo, 1 50 

Mahan's Civil Eugiueering. (Wood.) 8vo, 5 00 

Merriman and Brook's Handbook for Surveyors 12mo, mor., 2 00 

Merriman's Geodetic Surveying 8vo, 2 00 

" Retaining Walls and Masonry Dams 8vo, 2 00 

Mosely's Mechanical Engineering. (Mahan.) 8vo, 5 00 

IsTagle's Manual for Railroad Engineers .12mo, morocco, 3 00 

Patton's Civil Engineering 8vo, 7 50 

" Foundations 8vo, 5 00 

Rockwell's Roads and Pavements in France 12mo, 1 25 

Ruffuer's Non-tidal Rivers 8vo, 1 25 

Searles's Field Engineering 12mo, morocco flaps, 3 00 

" Railroad Spiral 12mo, morocco flaps, 1 50 

Siebert and Biggin's Modern Stone Cutting and Masonry. . .8vo, 1 50 

Smith's Cable Tramways 4to, 2 50 

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Spalding's Roads 'and Pavements 12mo, 2 00 

Hydraulic Cement 12mo, 2 00 

Thurston's Materials of Construction 8vo, 5 00 

* Trautwine's Civil Engineer's Pocket-book. ..12mo, mor. flaps, 5 00 

* " Cross-section Sheet, 25 

* ♦ ' Excavations and Embankments 8vo, 2 00 

* . " Laying Out Curves 12mo, morocco, 2 50 

Waddell's De Pontibus (A Pocket-book for Bridge Engineers). 

12mo, morocco, 3 00 

Wait's Engineering and Architectural Jurisprudence 8vo, 6 00 

Sheep, 6 50 

Warren's Stereotomy — Stone Cutting 8vo, 2 50 

Webb's Engineering Instruments 12mo, morocco, 1 00 

Wegmann's Construction of Masonry Dams 4to, 5 00 

Wellington's Location of Railways. 8vo, 5 00 

8 



Wheeler's Civil Eugineeriug 8vo, $4 00 

Wolff's Windmill as a Prime Mover 8vo, 3 00 

HYDRAULICS. 
Water-wheels — Windmills — Service Pipe — Drainage, Etc. 
{See also Engineering, p. 6.) 
Bazin's Experiments upon the Contraction of the Liquid Vein 

(Trautwine) 8vo, 2 00 

Bovey's Treatise on Hydraulics. Svo, 4 00 

Coffin's Graphical Solution of Hydraulic Problems 12mo, 2 50 

Perrel's Treatise on the Winds, Cyclones, and Tornadoes. . .8vo, 4 00 

Fuerte's Water and Public Health 12mo, 1 50 

Oanguillet&Kutter's Flow of Water. (Hering& Trautwine.). Svo, 4 00 

Hazeu's Filtration of Public Water Supply Svo, 2 00 

Herschel's 115 Experiments Svo, 2 00 

Kiersted's Sewage Disposal 12mo, 1 25 

Kirkwood's Lead Pipe for Service Pipe Svo, 1 50 

Mason's Water Supply Svo, 5 00 

3Ierriman's Treatise on Hydraulics. Svo, 4 00 

IS"ichols's Water Supply (Chemical and Sanitary) Svo, 2 50 

Ruffner's Improvement for Non-tidal Rivers Svo, 1 25 

Wegmann's Water Supply of the City of Kew York 4to, 10 00 

Weisbach's Hydraulics. (Du Bois.) Svo, 5 00 

Wilson's Irrigation Engineering Svo, 4 00 

Wolff's Windmill as a Prime Mover Svo, 3 00 

Wood's Theory of Turbines Svo. 2 50 

MANUFACTURES. 

Aniline — Boilers— Explosives— Iron— Sugar — Watches- 
Woollens, Etc. 

Allen's Tables for Iron Analysis Svo, 3 00 

Beaumont's Woollen and Worsted !>L^nufacture 12mo, 1 50 

Bolland's Encyclopaedia of Founding Terms 12mo, 3 00 

The Iron Founder 12mo, 2 50 

" " " " Supplement 12mo, 2 50 

Booth's Clock and Watch Makers Manual 12mo, 2 00 

Bouvier's Handbook on Oil Painting 12mo, 2 00 

Eissler's Explosives, Nitroglycerine and Dynamite Svo, 4 00 

Ford's Boiler Making for Boiler Makers ISmo, 1 00 

Metcalfe's Cost of Manufactures Svo, 5 00 



Melcalf s Steel— A Manual for Steel Users 12mo, $2 00 

Reiraann's Aniline Colors. (Crookes.) 8vo, 2 50 

* Reisig's Guide to Piece Dyeing 8vo, 25 00 

Spencer's Sugar Manufacturer's Handbook 12mo, inor. flap, 2 00 

" Handbook for Cbemists of Beet Houses. 

12mo, nior. flap, 3 00 

Svedelius's Handbook for Charcoal Burners 12mo, 1 50 

The Lathe and Its Uses 8vo, 6 00 

Thurston's Manual of Steam Boilers Bvo, 5 00 

Walke's Lectures on Explosives Svo, 4 00 

West's American Foundry Practice 12mo, 2 50 

" Moulder's Text-book 12mo, 2 50 

Wiechmaun's Sugar Analysis Svo, 2 50 

Woodbury's Fire Protection of Mills Svo, 2 50 



MATERIALS OF ENGINEERING. 

Streis!GTh — Elasticity — Resistance, Etc. 
{See also Engineering, p. 6.) 

Baker's Masonry Construction Svo, 

Beardslee and Kent's Strength of Wrought Iron Svo, 

Bovey's Strength of Materials Svo, 

Burr's Elasticity and Resistance of Materials Svo, 

Byrne's Highway Construction Svo, 

Carpenter's Testing Machines and Methods of Testing Materials. 

Church's Mechanics of Engineering — Solids and Fluids Svo, 

Du Bois's Stresses in Framed Structures 4to, 

Hatfield's Transverse Strains Svo, 

Johnson's Materials of Construction Svo, 

Lanza's Applied Mechanics Svo, 

" Strength of Wooden Columns Svo, paper, 

Merrill's Stones for Building and Decoration Svo, 

Merr im an's Mechanics of Materials Svo, 

' ' Strength of Materials •, . . 12mo, 

Pattou's Treatise on Foundations Svo, 

Rockwell's Roads and Pavements in France 12mo, 

Spalding's Roads and Pavements 12mo, 

Thurston's Materials of Construction Svo, 

10 



5 00 


1 50 


7 50 


5 00 


5 00 


6' 00 


10 00 


5 00 


6 00 


7 50 


50 


5 00 


4 00 


1 00 


5 00 


1 25 


2 00 


5 00 



Thurston's Materials of Eogiueeriug- 3 vols., 8vo, $8 00 

Vol. I., Xon-metallic 8vo, 3 00 

Vol. II., Iron and Steel • Bvo, 3 50 

Vol. III., Alloys, Brasses, and Bronzes Bvo, 2 50 

Weyraucb's Strength of Iron and Steel. (Du Bois.) 8vo, 1 50 

Wood's Resistance of Materials 8vo, 2 00 

MATHEMATICS. 

Calculus— Geometry— Trigonometry, Etc. 

Baker's Elliptic Functions 8vo, 1 50 

Ballard's Pyramid Problem 8vo, 1 50 

Barnard's Pyramid Problem 8vo, 1 50 

Bass's Differential Calculus 12mo, 4 00 

Brigg's Plane Analytical Geometrj' 12mo, 1 00 

Chapman's Theory of Equations 12mo, 1 50 

Chessin's Elements of the Theory of Functions. 

Compton's Logarithmic Computations 12mo, 1 50 

Craig's Linear Differential Equations , 8vo, 5 00 

Davis's Introduction to the Logic of Algebra 8vo, 1 50 

Halsted's Elements of Geometry ,..8vo, 1 75 

" Synthetic Geometry 8vo, 150 

Johnson's Curve Tracing 12mo, 1 00 

" Differential Equations — Ordinary and Partial 8vo, 3 50 

" Integral Calculus 12mo, 1 50 

" " " Unabridged. 

" Least Squares 12mo, 1 50 

Ludlow's Logarithmic and Other Tables. (Bass.) 8vo, 2 00 

Trigonometry with Tables. (Bass.) 8vo, 3 00 

Mahan's Descriptive Geometry (Stone Cutting) .8vo, 1 50 

Merriman and Woodward's Higher Mathematics 8vo, 5 00 

Merriman's Method of Least Squares 8vo, 2 00 

Parker's Quadrature of the Circle 8vo, 2 50 

Rice and Johnson's Differential and Integral Calculus, 

2 vols, inl, 12mo, 2 50 

Differential Calculus 8vo, 3 00 

" Abridgment of Differential Calculus.... 8vo, 150 

Searles's Elements of Geometry 8vo, 1 50 

Totten's Metrology 8vo, 2 50 

Warren's Descriptive Geometry 2 vols., 8vo, 3 50 

" Drafting Instruments 12mo, 125 

" Free-hand Drawing 12mo, 100 

" Higher Linear Perspective -. 8vo, 3 50 

" Linear Perspective 12mo, 100 

" Primary Geometry 12mo, 75 

11 



Dana's Descriptive Mineralogy. (E, S.) • • • -Svo, half morocco, ^12 50 

" Mineralogy and Petrography (J.D.) 12mo, 2 00 

" Minerals and How to Study Them. (E. S.) 12mo, 1 50 

" Text-book of Mineralogy. (E. S.) 8vo, 3 50 

^Drinker's Tunnelling, Explosives, Compounds, and Rock Drills. 

4to, half morocco, 25 00 

Egleston's Catalogue of ]\[iuerals and Synonyms 8vo, 2 50 

Eissler's Explosives — Nitroglycerine and Dynamite 8vo, 4 00 

Goodyear's Coal Mines of the Western Coast 12mo, 2 50 

Hussak's Rock- forming Minerals. (Smith.) 8vo, 2 00 

Ihlseng's Manual of Mining 8vo, 4 00 

Kuuhardt's Ore Dressing in Europe 8vo, 1 50 

O'Driscoll's Treatment of Gold Ores 8vo, 2 00 

Rosenbusch's Microscopical Physiography of Minerals and 

Rocks. (Iddings.) 8vo, 5 00 

Sawyer's Accidents in Mines 8vo, 7 00 

Stockbridge's Rocks and Soils 8vo, 2 50 

Walke's Lectures on Explosives. 8vo, 4 00 

Williams's Lithology 8vo, 3 00 

Wilson's Mine "Ventilation 16mo, 1 25 

" Placer Mining 12mo. 

STEAM AND ELECTRICAL ENGINES, BOILERS, Etc. 

Stationary — Marine— Locomotive — Gas Engines, Etc. 

{See also Engineering, p. 6.) 

Baldwin's Steam Heating for Buildings 12mo, 

Clerk's Gas Engine 12mo, 

Ford's Boiler Making for Boiler Makers 18mo, 

Hemen way's Indicator Practice 12mo, 

Hoadley's Warm-blast Furnace 8vo, 

Kneass's Practice and Theory of the Injector 8vo, 

MacCord's Slide Yalve 8yo, 

*3Iaw's Marine Engines Folio, half morocco, 

Meyer's Modern Locomotive Construction 4to, 

Peabody and Miller's Steam Boilers 8vo, 

Peabody's Tables of Saturated Steam 8vo, 

" Thermodynamics of the Steam Engine 8vo, 

Yalve Gears for the Steam-Engine 8vo, 

Pray's Twenty Years with the Indicator Royal 8vo, 

Pupin and Osterberg's Thermodynamics 12mo, 

Reagan's Steam and Electrical Locomotives 12mo, 

Rontgen's Thermodynamics. (Du Bois.) 8vo, 

Sinclair's Locomotive Running 12mo, 

Thurston's Boiler Explosion 12mo, 

14 



2 50 


4 00 


1 00 


2 00 


1 50 


1 50 


2 00 


:8 00 


.0 00 


4 00 


1 00 


5 00 


2 50 


2 50 


1 25 


2 00 


5 00 


3 00 


1 50 



Tliurston's Engine and Boiler Trials 8vo, $5 00 

" Manual of the Steam Engine. Part I., Structure 

and Theory. 8vo, 7 50 

** Manual of the Steam Engine. Part II., Design, 

Construction, and Operation 8vo, 7 50 

2 parts, 12 00 

** Philosophy of the Steam Engine 12mo, 75 

" Reflection on the Motive Power of Heat. (Caruot.) 

12mo. 1 50 

" Stationary Steam Engines 12mo, 1 50 

" Steam-boiler Construction and Operation 8vo, 5 00 

Spangler's Valve Gears 8vo, 2 50 

Trowbridge's Stationary Steam Engines 4to, boards, 2 50 

Weisbach's Steam Engine. (Du Bois.) 8vo, 5 00 

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Wilson's Steam Boilers. (Flather.) 12mo, 2 50 

Wood's Thermodynamics, Heat Motors, etc 8vo, 4 00 

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For Actuaries, Chemists, Engineers, Mechanics— Metric 
Tables, Etc. 

Adriance's Laboratory Calculations 12mo, 1 25 

Allen's Tables for Iron Analysis 8vo, 3 00 

Bixb3^'s Graphical Computing Tables Sheet, 25 

Conipton's Logarithms 12mo, 1 50 

Crandall's Railway and Earthwork Tables 8vo, 1 50 

Egleston's Weights and Measures 18mo, 75 

Fisher's Table of Cubic Yards Cardboard, 25 

Hudson's Excavation Tables. Vol. II 8vo, 1 00 

Johnson's Stadia and Earthwork Tables , 8vo, 1 25 

Ludlow's Logarithmic and Other Tables. (Bass.) 12mo, 2 00 

Thurston's Conversion Tables 8vo, 1 00 

Tott^n's Metrology 8vo, 2 50 

VENTILATION. 

Steam Heating — House Inspection — Mine Ventilation. 

Baldwin's Steam Heating 12mo, 2 50 

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Gerhard's Sanitary House Inspection Square 16mo, 1 00 

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Wilson's Mine Ventilation 16mo, 1 25 

15 



niSCELLANEOUS PUBLICATIONS. 

Alcott's Gems, Sentiment, Language Gilt edges, $o 00 

Bailey's The Xew Tale of a Tub , 8vo, 75 

Ballard's Solution of the Pyramid Problem 8vo, 1 50 

Barnard's The Metrological System of the Great Pyramid. .8vo, 1 50 

Davis's Elements of Law Svo, 3 GO 

Emmon's Geological Guide-book of the Rocky Mountains. .Svo, 1 50 

Ferrel's Ti-eatise on the Winds Svo, 4 00 

Haines's Addresses Delivered before[the Am. Ry. Assn. ..12mo. 2 50 

Mott's The Fallacy of the Present Theory of Sound . .Sq. 16mo, 1 GO 

Perkins's Cornell University Oblong 4to, 1 50 

Ricketts's History of "Rensselaer Polytechnic Institute Svo, 3 00 

Rotherham's The New Testament Criticall}' Emphasized. 

12mo, 1 Sa 
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Large Svo, 2 GO 

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Whitehouse's Lake Mceris Paper, 25 

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Mott's Composition, Digestibility, and Nutritive Value of Food. 

Large mounted chart, 1 25 

Ruddiman's Incompatibilities in Prescriptions Svo, 2 GO 

Steel's Treatise on the Diseases of the Ox Svo, 6 00 

" Treatise on the Diseases of the Dog Svo, 3 50 

Worcester's Small Hospitals — Establishment and Maintenance, 
including Atkinson's Suggestions for Hospital Archi- 
tecture 12mo, 1 25 

16 



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